Details

analyze1.5s (9.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample11.1s (74.8%)

Results

3.5s	3995×	body	1024	valid
3.2s	3932×	body	1024	invalid
1.3s	2060×	body	512	invalid
1.2s	1979×	body	512	valid
764.0ms	516×	body	2048	valid
457.0ms	1067×	body	256	invalid
453.0ms	1069×	body	256	valid
157.0ms	697×	body	128	valid
2.0ms	2×	body	2048	invalid
1.0ms	3×	body	128	invalid

preprocess30.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

569×	`fma-def_binary64`
323×	`fma-neg_binary64`
202×	`distribute-rgt-in_binary64`
192×	`cancel-sign-sub-inv_binary64`
175×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	122	59
3	326	55
4	975	55
5	2553	55
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs

(neg.f64 (*.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))

Outputs
(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))
(.f64 (neg.f64 (.f64 (/.f64 1 (PI.f64)) 4)) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (exp.f64 (.f64 (/.f64 (PI.f64) 4) (neg.f64 f)))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (exp.f64 (.f64 (/.f64 (PI.f64) 4) (neg.f64 f)))))))
(*.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) (neg.f64 f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) (neg.f64 f))))) (neg.f64 (/.f64 4 (PI.f64))))
(*.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) (neg.f64 f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) (neg.f64 f))))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 f) (/.f64 (PI.f64) 4)) (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f)))) (-.f64 (pow.f64 (exp.f64 f) (/.f64 (PI.f64) 4)) (exp.f64 (.f64 -1/4 (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (.f64 -1/4 (PI.f64))) f)) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (*.f64 -1/4 (PI.f64))) f)))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 38 to 30 computations (21.1% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
323×	`fma-neg_binary64`
202×	`distribute-rgt-in_binary64`
192×	`cancel-sign-sub-inv_binary64`
175×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	122	59
3	326	55
4	975	55
5	2553	55

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs

(neg.f64 (*.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (*.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))

Outputs
(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))
(.f64 (neg.f64 (.f64 (/.f64 1 (PI.f64)) 4)) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (exp.f64 (.f64 (/.f64 (PI.f64) 4) (neg.f64 f)))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (exp.f64 (.f64 (/.f64 (PI.f64) 4) (neg.f64 f)))))))
(*.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) (neg.f64 f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) (neg.f64 f))))) (neg.f64 (/.f64 4 (PI.f64))))
(*.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) (neg.f64 f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) (neg.f64 f))))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 f) (/.f64 (PI.f64) 4)) (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f)))) (-.f64 (pow.f64 (exp.f64 f) (/.f64 (PI.f64) 4)) (exp.f64 (.f64 -1/4 (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (.f64 -1/4 (PI.f64))) f)) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 (*.f64 -1/4 (PI.f64))) f)))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

62.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	62.1b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Status

Error

Program

▶

62.1b

(*.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 136 to 100 computations (26.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
✓	0.3b	(*.f64 (PI.f64) f)
✓	1.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
✓	5.4b	(-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))

series100.0ms (0.7%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
47.0ms	f	@	-inf	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
39.0ms	f	@	inf	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
4.0ms	f	@	0	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
4.0ms	f	@	0	(-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))
1.0ms	f	@	0	(/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

195×	`add-sqr-sqrt_binary64`
191×	`pow1_binary64`
189×	`*-un-lft-identity_binary64`
188×	`add-log-exp_binary64`
185×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	128
1	397	128

Stop Event

1×	node limit

Counts

4 → 120

Calls

Call 1

Inputs
(-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f)))
(/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
(*.f64 (PI.f64) f)
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (cbrt.f64 (pow.f64 (exp.f64 -1/2) (.f64 (PI.f64) f))) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 (neg.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (sqrt.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (neg.f64 (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)) 1))) (fma.f64 (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) 1 (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f)) 2) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f)) (neg.f64 (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)) 1))) (fma.f64 (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) 1 (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f)) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f)) (neg.f64 (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)) 1))) (fma.f64 (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) 1 (.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) 1) (.f64 (neg.f64 (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) 2) (cbrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 (PI.f64)) 1/4) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 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simplify51.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
610×	`fma-def_binary64`
311×	`distribute-rgt-in_binary64`
297×	`distribute-lft-in_binary64`
167×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	1691
1	426	1557
2	1623	1463

Stop Event

1×	node limit

Counts

168 → 151

Calls

Call 1

Inputs
(.f64 (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64))) f)
(+.f64 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f) (.f64 (pow.f64 f 3) (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3)))))
(+.f64 (.f64 (pow.f64 f 5) (-.f64 (.f64 1/122880 (pow.f64 (PI.f64) 5)) (.f64 -1/122880 (pow.f64 (PI.f64) 5)))) (+.f64 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f) (.f64 (pow.f64 f 3) (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (*.f64 -1/384 (pow.f64 (PI.f64) 3))))))
(+.f64 (.f64 (pow.f64 f 5) (-.f64 (.f64 1/122880 (pow.f64 (PI.f64) 5)) (.f64 -1/122880 (pow.f64 (PI.f64) 5)))) (+.f64 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f) (+.f64 (.f64 (pow.f64 f 3) (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3)))) (.f64 (pow.f64 f 7) (-.f64 (.f64 1/82575360 (pow.f64 (PI.f64) 7)) (.f64 -1/82575360 (pow.f64 (PI.f64) 7)))))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(/.f64 2 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64))) f))
(+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (+.f64 (.f64 2 (/.f64 1 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f))) (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))))
(+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (+.f64 (.f64 2 (/.f64 1 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f))) (+.f64 (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 f (-.f64 (.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 2 (/.f64 (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3))) (pow.f64 (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64))) 2))))))))
(+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (+.f64 (.f64 (pow.f64 f 2) (-.f64 (+.f64 (.f64 1/384 (/.f64 (pow.f64 (PI.f64) 3) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 -1/384 (/.f64 (pow.f64 (PI.f64) 3) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))) (/.f64 (.f64 (+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))) (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3)))) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))) (+.f64 (.f64 2 (/.f64 1 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f))) (+.f64 (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 f (-.f64 (.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 2 (/.f64 (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3))) (pow.f64 (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64))) 2)))))))))
(/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(*.f64 f (PI.f64))
(.f64 -4 (/.f64 (+.f64 (log.f64 (/.f64 2 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 -1 (log.f64 f))) (PI.f64)))
(+.f64 (.f64 -4 (/.f64 (+.f64 (log.f64 (/.f64 2 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 -1 (log.f64 f))) (PI.f64))) (.f64 -2 (/.f64 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) (.f64 f (+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64)))))))) (PI.f64))))
(+.f64 (.f64 -4 (/.f64 (+.f64 (log.f64 (/.f64 2 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 -1 (log.f64 f))) (PI.f64))) (+.f64 (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (pow.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) 2) (pow.f64 (+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))) 2))) (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) (-.f64 (.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 2 (/.f64 (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3))) (pow.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) 2)))))) (pow.f64 f 2)) (PI.f64))) (.f64 -2 (/.f64 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) (.f64 f (+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))))) (PI.f64)))))
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(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))

Outputs
(.f64 (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64))) f)
(.f64 (.f64 (PI.f64) 1/2) f)
(.f64 (PI.f64) (.f64 1/2 f))
(.f64 (PI.f64) (.f64 f 1/2))
(+.f64 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f) (.f64 (pow.f64 f 3) (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3)))))
(fma.f64 (.f64 (PI.f64) 1/2) f (.f64 (pow.f64 f 3) (*.f64 (pow.f64 (PI.f64) 3) 1/192)))
(fma.f64 (.f64 (PI.f64) 1/2) f (.f64 (pow.f64 (PI.f64) 3) (*.f64 1/192 (pow.f64 f 3))))
(fma.f64 (PI.f64) (.f64 f 1/2) (.f64 (pow.f64 (PI.f64) 3) (*.f64 1/192 (pow.f64 f 3))))
(+.f64 (.f64 (pow.f64 f 5) (-.f64 (.f64 1/122880 (pow.f64 (PI.f64) 5)) (.f64 -1/122880 (pow.f64 (PI.f64) 5)))) (+.f64 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f) (.f64 (pow.f64 f 3) (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (*.f64 -1/384 (pow.f64 (PI.f64) 3))))))
(fma.f64 (pow.f64 f 5) (.f64 (pow.f64 (PI.f64) 5) 1/61440) (fma.f64 (.f64 (PI.f64) 1/2) f (.f64 (pow.f64 f 3) (.f64 (pow.f64 (PI.f64) 3) 1/192))))
(fma.f64 (pow.f64 f 5) (.f64 (pow.f64 (PI.f64) 5) 1/61440) (fma.f64 (.f64 (PI.f64) 1/2) f (.f64 (pow.f64 (PI.f64) 3) (.f64 1/192 (pow.f64 f 3)))))
(fma.f64 (PI.f64) (.f64 f 1/2) (fma.f64 (pow.f64 (PI.f64) 3) (.f64 1/192 (pow.f64 f 3)) (.f64 (pow.f64 (PI.f64) 5) (.f64 1/61440 (pow.f64 f 5)))))
(+.f64 (.f64 (pow.f64 f 5) (-.f64 (.f64 1/122880 (pow.f64 (PI.f64) 5)) (.f64 -1/122880 (pow.f64 (PI.f64) 5)))) (+.f64 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f) (+.f64 (.f64 (pow.f64 f 3) (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3)))) (.f64 (pow.f64 f 7) (-.f64 (.f64 1/82575360 (pow.f64 (PI.f64) 7)) (.f64 -1/82575360 (pow.f64 (PI.f64) 7)))))))
(fma.f64 (pow.f64 f 5) (.f64 (pow.f64 (PI.f64) 5) 1/61440) (fma.f64 (.f64 (PI.f64) 1/2) f (fma.f64 (pow.f64 f 3) (.f64 (pow.f64 (PI.f64) 3) 1/192) (.f64 (pow.f64 f 7) (*.f64 (pow.f64 (PI.f64) 7) 1/41287680)))))
(fma.f64 (pow.f64 f 5) (.f64 (pow.f64 (PI.f64) 5) 1/61440) (fma.f64 (.f64 (PI.f64) 1/2) f (fma.f64 (pow.f64 f 7) (.f64 (pow.f64 (PI.f64) 7) 1/41287680) (.f64 (pow.f64 (PI.f64) 3) (*.f64 1/192 (pow.f64 f 3))))))
(fma.f64 (pow.f64 f 5) (.f64 (pow.f64 (PI.f64) 5) 1/61440) (fma.f64 (pow.f64 f 3) (.f64 (pow.f64 (PI.f64) 3) 1/192) (fma.f64 (PI.f64) (.f64 f 1/2) (.f64 (pow.f64 f 7) (*.f64 (pow.f64 (PI.f64) 7) 1/41287680)))))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
(-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))))
(-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
(/.f64 2 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64))) f))
(/.f64 2 (.f64 (.f64 (PI.f64) 1/2) f))
(/.f64 2 (.f64 (PI.f64) (.f64 1/2 f)))
(/.f64 (/.f64 2 f) (*.f64 (PI.f64) 1/2))
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(/.f64 2 (.f64 (.f64 (PI.f64) 1/2) f))
(/.f64 2 (.f64 (PI.f64) (.f64 1/2 f)))
(/.f64 (/.f64 2 f) (*.f64 (PI.f64) 1/2))
(+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (+.f64 (.f64 2 (/.f64 1 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f))) (+.f64 (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 f (-.f64 (.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 2 (/.f64 (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3))) (pow.f64 (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64))) 2))))))))
(fma.f64 -1/4 (/.f64 (PI.f64) (.f64 (PI.f64) 1/2)) (+.f64 (/.f64 2 (.f64 (.f64 (PI.f64) 1/2) f)) (fma.f64 1/4 (/.f64 (PI.f64) (.f64 (PI.f64) 1/2)) (.f64 f (+.f64 (.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (.f64 (PI.f64) 1/2))) (.f64 -2 (/.f64 (.f64 (pow.f64 (PI.f64) 3) 1/192) (pow.f64 (.f64 (PI.f64) 1/2) 2))))))))
(+.f64 (+.f64 (/.f64 2 (.f64 (PI.f64) (.f64 1/2 f))) 0) (.f64 f (fma.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (.f64 (PI.f64) 1/2)) (.f64 (/.f64 (pow.f64 (PI.f64) 3) (/.f64 (.f64 (pow.f64 (PI.f64) 2) 1/4) 1/192)) -2))))
(+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2))))
(+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (+.f64 (.f64 (pow.f64 f 2) (-.f64 (+.f64 (.f64 1/384 (/.f64 (pow.f64 (PI.f64) 3) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 -1/384 (/.f64 (pow.f64 (PI.f64) 3) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))) (/.f64 (.f64 (+.f64 (.f64 -1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))) (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3)))) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64)))))) (+.f64 (.f64 2 (/.f64 1 (.f64 (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))) f))) (+.f64 (.f64 1/4 (/.f64 (PI.f64) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 f (-.f64 (.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (-.f64 (.f64 1/4 (PI.f64)) (.f64 -1/4 (PI.f64))))) (.f64 2 (/.f64 (-.f64 (.f64 1/384 (pow.f64 (PI.f64) 3)) (.f64 -1/384 (pow.f64 (PI.f64) 3))) (pow.f64 (-.f64 (.f64 1/4 (PI.f64)) (*.f64 -1/4 (PI.f64))) 2)))))))))
(fma.f64 -1/4 (/.f64 (PI.f64) (.f64 (PI.f64) 1/2)) (+.f64 (/.f64 2 (.f64 (.f64 (PI.f64) 1/2) f)) (fma.f64 1/4 (/.f64 (PI.f64) (.f64 (PI.f64) 1/2)) (.f64 f (+.f64 (.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (.f64 (PI.f64) 1/2))) (.f64 -2 (/.f64 (.f64 (pow.f64 (PI.f64) 3) 1/192) (pow.f64 (.f64 (PI.f64) 1/2) 2))))))))
(+.f64 (+.f64 (/.f64 2 (.f64 (PI.f64) (.f64 1/2 f))) 0) (.f64 f (fma.f64 1/16 (/.f64 (pow.f64 (PI.f64) 2) (.f64 (PI.f64) 1/2)) (.f64 (/.f64 (pow.f64 (PI.f64) 3) (/.f64 (.f64 (pow.f64 (PI.f64) 2) 1/4) 1/192)) -2))))
(+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2))))
(/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
(/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))))
(/.f64 (+.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
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(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (PI.f64)))
(/.f64 -4 (/.f64 (PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))))))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (.f64 f (PI.f64))))) (-.f64 (exp.f64 (.f64 1/4 (.f64 f (PI.f64)))) (exp.f64 (.f64 -1/4 (*.f64 f (PI.f64))))))) (PI.f64)))
(.f64 -4 (/.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (PI.f64)))
(/.f64 -4 (/.f64 (PI.f64) (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 1/4) (.f64 (PI.f64) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))))))

prune222.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	4	169

Error

1.2b

Counts

169 → 4

Alt Table

Status	Error	Program
	1.5b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 (PI.f64) (.f64 f 1/2) (fma.f64 (pow.f64 (PI.f64) 3) (.f64 1/192 (pow.f64 f 3)) (.f64 (pow.f64 (PI.f64) 5) (.f64 1/61440 (pow.f64 f 5))))))) (/.f64 -4 (PI.f64)))
	1.4b	(.f64 (log.f64 (+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2))))) (/.f64 -4 (PI.f64)))
▶	1.3b	(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (.f64 -2 (fma.f64 (/.f64 (fma.f64 (.f64 (PI.f64) 1/2) (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0) (PI.f64)) (*.f64 f f) 0)))
	1.7b	(/.f64 -4 (/.f64 (PI.f64) (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f))))

Compiler

Compiled 7679 to 5086 computations (33.8% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 (.f64 (PI.f64) 1/2) (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0)
✓	1.0b	(pow.f64 (PI.f64) 3)
✓	1.0b	(*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48)
✓	2.0b	(log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2)))

series0.0ms (0%)

Counts: 4 → 0

rewrite75.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`prod-diff_binary64`
192×	`add-sqr-sqrt_binary64`
184×	`add-log-exp_binary64`
182×	`add-cbrt-cube_binary64`
182×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	41
1	471	37
2	4857	37

Stop Event

1×	node limit

Counts

4 → 127

Calls

Call 1

Inputs
(log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2)))
(*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48)
(pow.f64 (PI.f64) 3)
(fma.f64 (.f64 (PI.f64) 1/2) (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (/.f64 4 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 2) (log.f64 (/.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 2) (neg.f64 (log.f64 (.f64 (PI.f64) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (/.f64 4 (PI.f64)))) (log.f64 (sqrt.f64 (/.f64 4 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 4 (PI.f64))) 2)) (log.f64 (cbrt.f64 (/.f64 4 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (log.f64 2) (neg.f64 (.f64 (log.f64 (.f64 (PI.f64) 1/2)) 1))) (fma.f64 (neg.f64 (log.f64 (.f64 (PI.f64) 1/2))) 1 (.f64 (log.f64 (.f64 (PI.f64) 1/2)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (cbrt.f64 (log.f64 2)) (cbrt.f64 (log.f64 2))) (cbrt.f64 (log.f64 2)) (neg.f64 (.f64 (log.f64 (.f64 (PI.f64) 1/2)) 1))) (fma.f64 (neg.f64 (log.f64 (.f64 (PI.f64) 1/2))) 1 (.f64 (log.f64 (.f64 (PI.f64) 1/2)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (log.f64 2)) (sqrt.f64 (log.f64 2)) (neg.f64 (.f64 (log.f64 (.f64 (PI.f64) 1/2)) 1))) (fma.f64 (neg.f64 (log.f64 (.f64 (PI.f64) 1/2))) 1 (.f64 (log.f64 (.f64 (PI.f64) 1/2)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (log.f64 2) (neg.f64 (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (cbrt.f64 (log.f64 2)) (cbrt.f64 (log.f64 2))) (cbrt.f64 (log.f64 2)) (neg.f64 (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (log.f64 2)) (sqrt.f64 (log.f64 2)) (neg.f64 (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (log.f64 (.f64 (PI.f64) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (log.f64 2) (neg.f64 (log.f64 (.f64 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1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 4 (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (/.f64 2 (PI.f64))) (log.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (log.f64 (/.f64 4 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (log.f64 (/.f64 4 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (log.f64 (/.f64 4 (PI.f64)))) (pow.f64 (cbrt.f64 (log.f64 (/.f64 4 (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 4 (PI.f64)))) 2) (cbrt.f64 (log.f64 (/.f64 4 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (log.f64 (/.f64 4 (PI.f64)))) (sqrt.f64 (log.f64 (/.f64 4 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log.f64 (.f64 (PI.f64) 1/2)) 3)) (+.f64 (.f64 (log.f64 2) (log.f64 2)) (+.f64 (.f64 (log.f64 (.f64 (PI.f64) 1/2)) (log.f64 (.f64 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) 1/48))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (PI.f64) 3) (/.f64 (pow.f64 (PI.f64) 2) 1/48))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/48 (/.f64 1 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (PI.f64) 2) (.f64 (pow.f64 (PI.f64) 3) 1/48)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (PI.f64) 3) 1/48) (pow.f64 (PI.f64) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (pow.f64 (PI.f64) 3) 1/48)) (neg.f64 (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (PI.f64) 3) 1/48) (PI.f64)) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (PI.f64) 3) 1/48) 1) (pow.f64 (PI.f64) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (PI.f64) 3) 1/48) (cbrt.f64 (pow.f64 (PI.f64) 4))) (pow.f64 (cbrt.f64 (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (pow.f64 (PI.f64) 3)) 1/48) (neg.f64 (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/48 (neg.f64 (pow.f64 (PI.f64) 3))) (neg.f64 (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) 1/48) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) 1/48) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) 1/48)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) 1/48)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (PI.f64) 2) 1/2304))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/48) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) 1/48))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) 1/48) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) 1/48)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) 1/48)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) 1/48)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) 1/48)))))))
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/16 (.f64 2 (PI.f64))) (.f64 (PI.f64) 1/2)) (.f64 (.f64 (PI.f64) -1/24) (.f64 (PI.f64) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 1/16 (.f64 2 (PI.f64)))) (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (PI.f64) (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) 1/2) (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)) (.f64 (PI.f64) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (PI.f64) 2) 1/4)) (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 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-1/24))) 2)) (cbrt.f64 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 (PI.f64) 1/2) (sqrt.f64 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) (sqrt.f64 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 3) 0) (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 2) (-.f64 0 (.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 2) 0) (-.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 1/2)) (log.f64 (fma.f64 1/16 (.f64 2 (PI.f64)) (.f64 (PI.f64) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) (.f64 1/2 (fma.f64 1/16 (.f64 2 (PI.f64)) (*.f64 (PI.f64) -1/24))))))))))

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

127 → 127

Calls

Call 1

Inputs

Outputs

prune557.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	127	4	131

Error

1.2b

Counts

131 → 4

Alt Table

Status	Error	Program
	1.5b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 (PI.f64) (.f64 f 1/2) (fma.f64 (pow.f64 (PI.f64) 3) (.f64 1/192 (pow.f64 f 3)) (.f64 (pow.f64 (PI.f64) 5) (.f64 1/61440 (pow.f64 f 5))))))) (/.f64 -4 (PI.f64)))
▶	1.4b	(.f64 (log.f64 (+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2))))) (/.f64 -4 (PI.f64)))
✓	1.3b	(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (.f64 -2 (fma.f64 (/.f64 (fma.f64 (.f64 (PI.f64) 1/2) (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0) (PI.f64)) (*.f64 f f) 0)))
	1.7b	(/.f64 -4 (/.f64 (PI.f64) (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f))))

Compiler

Compiled 6319 to 4678 computations (26% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2))
✓	1.0b	(fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2))
	1.0b	(pow.f64 (PI.f64) 3)
	1.0b	(*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48)

series0.0ms (0%)

Counts: 2 → 0

rewrite53.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

253×	`prod-diff_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
145×	`add-sqr-sqrt_binary64`
140×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	15
1	371	15
2	3599	15

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

Inputs
(fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2))
(/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) -1/24) (*.f64 (*.f64 1/16 (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/16 (PI.f64)) 2) (*.f64 (PI.f64) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))) (cbrt.f64 (pow.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)) 2)) (cbrt.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))) (sqrt.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (*.f64 1/16 (PI.f64)) 2) 3) (pow.f64 (*.f64 (PI.f64) -1/24) 3)) (fma.f64 (*.f64 (*.f64 1/16 (PI.f64)) 2) (*.f64 (*.f64 1/16 (PI.f64)) 2) (-.f64 (*.f64 (pow.f64 (PI.f64) 2) 1/576) (*.f64 (*.f64 (*.f64 1/16 (PI.f64)) 2) (*.f64 (PI.f64) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (*.f64 1/16 (PI.f64)) 2) (*.f64 (*.f64 1/16 (PI.f64)) 2)) (*.f64 (pow.f64 (PI.f64) 2) 1/576)) (-.f64 (*.f64 (*.f64 1/16 (PI.f64)) 2) (*.f64 (PI.f64) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/16 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) -1/24))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) (*.f64 (pow.f64 (PI.f64) 2) (pow.f64 (PI.f64) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) 2) (*.f64 (PI.f64) (pow.f64 (PI.f64) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (PI.f64) 3)) (/.f64 1 (neg.f64 (pow.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (PI.f64)) (/.f64 (pow.f64 (PI.f64) 3) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -2) (pow.f64 (PI.f64) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) 3/2) (*.f64 (pow.f64 (PI.f64) 3/2) (pow.f64 (PI.f64) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (PI.f64) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) 1) (/.f64 (pow.f64 (PI.f64) 2) (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (PI.f64)) (/.f64 (pow.f64 (PI.f64) 2) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) 2) (PI.f64)) (/.f64 (PI.f64) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) 2) 1) (/.f64 (PI.f64) (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) 3/2) 1) (/.f64 (pow.f64 (PI.f64) 3/2) (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (PI.f64) 4))) (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (cbrt.f64 (PI.f64)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (cbrt.f64 (pow.f64 (PI.f64) 4))) (/.f64 (pow.f64 (PI.f64) 2) (pow.f64 (cbrt.f64 (PI.f64)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) 2) (cbrt.f64 (pow.f64 (PI.f64) 4))) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) 3/2) (cbrt.f64 (pow.f64 (PI.f64) 4))) (/.f64 (pow.f64 (PI.f64) 3/2) (pow.f64 (cbrt.f64 (PI.f64)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (PI.f64) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (PI.f64)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (PI.f64)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (PI.f64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (PI.f64) 3) (neg.f64 (pow.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (PI.f64) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (PI.f64) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (PI.f64)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x PI.f64)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (PI.f64)))))))

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

62 → 62

Calls

Call 1

Inputs

Outputs

prune413.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	117	4	121

Error

1.2b

Counts

121 → 4

Alt Table

Status	Error	Program
	1.5b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 (PI.f64) (.f64 f 1/2) (fma.f64 (pow.f64 (PI.f64) 3) (.f64 1/192 (pow.f64 f 3)) (.f64 (pow.f64 (PI.f64) 5) (.f64 1/61440 (pow.f64 f 5))))))) (/.f64 -4 (PI.f64)))
▶	1.4b	(.f64 (log.f64 (+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2))))) (/.f64 -4 (PI.f64)))
✓	1.3b	(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (.f64 -2 (fma.f64 (/.f64 (fma.f64 (.f64 (PI.f64) 1/2) (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0) (PI.f64)) (*.f64 f f) 0)))
	1.7b	(/.f64 -4 (/.f64 (PI.f64) (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f))))

Compiler

Compiled 4139 to 3238 computations (21.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2)))
✓	1.0b	(fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2))
✓	1.0b	(pow.f64 (exp.f64 1/48) (PI.f64))
✓	2.8b	(log.f64 (pow.f64 (exp.f64 1/48) (PI.f64)))

series78.0ms (0.5%)

Counts

4 → 12

Calls

3 calls:

Time

Variable

Point

Expression

77.0ms

(*.f64 f (fma.f64 1/16 (*.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2)))

1.0ms

inf

(*.f64 f (fma.f64 1/16 (*.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2)))

1.0ms

-inf

(*.f64 f (fma.f64 1/16 (*.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2)))

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`log-prod_binary64`
246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
201×	`log-pow_binary64`
152×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	323	41
2	3299	41

Stop Event

1×	node limit

Counts

4 → 107

Calls

Call 1

Inputs
(log.f64 (pow.f64 (exp.f64 1/48) (PI.f64)))
(pow.f64 (exp.f64 1/48) (PI.f64))
(fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2))
(.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/48 (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/48 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/24) (PI.f64)))) (.f64 1/3 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/3 (.f64 1/48 (PI.f64))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/24) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (.f64 1/48 (PI.f64))) (.f64 1/2 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 1 (PI.f64))) (.f64 1/48 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (exp.f64 1/72) (PI.f64))) (log.f64 (pow.f64 (exp.f64 1/144) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (exp.f64 1/96) (PI.f64))) (log.f64 (pow.f64 (exp.f64 1/96) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/48 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/48 (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (PI.f64) 1/48)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/48 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 1/48 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 1/48 (PI.f64))) (pow.f64 (cbrt.f64 (.f64 1/48 (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 1/48 (PI.f64))) 2) (cbrt.f64 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (PI.f64)) (log.f64 (pow.f64 (exp.f64 1/48) (pow.f64 (cbrt.f64 (PI.f64)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) 1/48))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 1/48 (PI.f64))) (sqrt.f64 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) 1/48))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) (log.f64 (pow.f64 (exp.f64 1/48) (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 1/2 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) 1/2) 1/24)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 3 (.f64 1/3 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/3 (.f64 3 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (PI.f64) 1/2 (.f64 (PI.f64) 1/2)) 1/48)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (.f64 (PI.f64) 1/2)) 1/48)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/48 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/48 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/48 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/48 (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/48 (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/48 (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (PI.f64) 2) 1/2304))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/48 (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/48 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/48 (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/48 (PI.f64))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (exp.f64 1/48) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 1/48) (PI.f64)))) (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 1/48) (PI.f64)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 1/48) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (exp.f64 1/48) (PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (exp.f64 1/48) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (exp.f64 1/48) (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 1/48) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (exp.f64 1/48) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) (cbrt.f64 (pow.f64 (exp.f64 1/24) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 1/24) (PI.f64))) (cbrt.f64 (pow.f64 (exp.f64 1/48) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) (sqrt.f64 (pow.f64 (exp.f64 1/48) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (PI.f64)) (pow.f64 (exp.f64 1/48) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 1/72) (PI.f64)) (pow.f64 (exp.f64 1/144) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 1/96) (PI.f64)) (pow.f64 (exp.f64 1/96) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 1/24) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 1/48) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (exp.f64 1/48) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 1/48) (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 1/48) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 1/48 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 1/48) (PI.f64))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) -1/24) (/.f64 1/16 (/.f64 1/2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))) (.f64 (PI.f64) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))))) (cbrt.f64 (exp.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))) (cbrt.f64 (pow.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 2)) (cbrt.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))) (sqrt.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))) 3) (pow.f64 (.f64 (PI.f64) -1/24) 3)) (fma.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))) (/.f64 1/16 (/.f64 1/2 (PI.f64))) (-.f64 (pow.f64 (.f64 (PI.f64) -1/24) 2) (.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))) (.f64 (PI.f64) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))) (/.f64 1/16 (/.f64 1/2 (PI.f64)))) (pow.f64 (.f64 (PI.f64) -1/24) 2)) (-.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))) (.f64 (PI.f64) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 (PI.f64) -1/24)) (exp.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) -1/24))) (exp.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) (+.f64 1 (expm1.f64 (.f64 (PI.f64) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))) f) (.f64 (.f64 (PI.f64) -1/24) f))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 f (/.f64 1/16 (/.f64 1/2 (PI.f64)))) (.f64 f (.f64 (PI.f64) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 f) (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))))) (cbrt.f64 (pow.f64 (exp.f64 f) (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 f) (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 f) (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 f) (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 f) (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 3) (pow.f64 f 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 f 3) (pow.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 f (/.f64 1/16 (/.f64 1/2 (PI.f64))) (.f64 f (.f64 (PI.f64) -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/16 (/.f64 1/2 (PI.f64))) f (.f64 (.f64 (PI.f64) -1/24) f))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (fma.f64 (PI.f64) -1/24 (/.f64 1/16 (/.f64 1/2 (PI.f64)))) f)))))))

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`fma-def_binary64`
18×	`*-commutative_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
6×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	96
1	23	96
2	50	96
3	86	96
4	90	96

Stop Event

1×

saturated

Counts

119 → 109

Calls

Call 1

Inputs
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))

Outputs
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))
(.f64 f (+.f64 (.f64 -1/24 (PI.f64)) (*.f64 1/8 (PI.f64))))
(.f64 f (.f64 (PI.f64) 1/12))
(.f64 (PI.f64) (.f64 f 1/12))

prune362.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	109	4	113

Error

1.2b

Counts

113 → 4

Alt Table

Status	Error	Program
	1.5b	(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 (PI.f64) (.f64 f 1/2) (fma.f64 (pow.f64 (PI.f64) 3) (.f64 1/192 (pow.f64 f 3)) (.f64 (pow.f64 (PI.f64) 5) (.f64 1/61440 (pow.f64 f 5))))))) (/.f64 -4 (PI.f64)))
✓	1.3b	(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (.f64 -2 (fma.f64 (/.f64 (fma.f64 (.f64 (PI.f64) 1/2) (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0) (PI.f64)) (*.f64 f f) 0)))
	1.7b	(/.f64 -4 (/.f64 (PI.f64) (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f))))
	1.4b	(.f64 (log.f64 (+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (log.f64 (pow.f64 (exp.f64 1/48) (sqrt.f64 (PI.f64))))) -2))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 3457 to 2704 computations (21.8% saved)

regimes33.0ms (0.2%)

Accuracy

Total -60.9b remaining (-4546.2%)

Threshold costs -60.9b (-4546.2%)

Counts

8 → 1

Calls

Call 1

Inputs
(.f64 (log.f64 (+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (log.f64 (pow.f64 (exp.f64 1/48) (sqrt.f64 (PI.f64))))) -2))))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (log.f64 (pow.f64 (exp.f64 1/48) (PI.f64))) -2))))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 (PI.f64) (.f64 f 1/2) (fma.f64 (pow.f64 (PI.f64) 3) (.f64 1/192 (pow.f64 f 3)) (.f64 (pow.f64 (PI.f64) 5) (.f64 1/61440 (pow.f64 f 5))))))) (/.f64 -4 (PI.f64)))
(.f64 (log.f64 (+.f64 (/.f64 (/.f64 2 f) (.f64 (PI.f64) 1/2)) (.f64 f (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2))))) (/.f64 -4 (PI.f64)))
(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (.f64 -2 (fma.f64 (/.f64 (fma.f64 (.f64 (PI.f64) 1/2) (fma.f64 1/16 (.f64 1 (/.f64 (PI.f64) 1/2)) (.f64 (.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0) (PI.f64)) (*.f64 f f) 0)))
(/.f64 -4 (/.f64 (PI.f64) (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f))))
(.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (pow.f64 (exp.f64 (/.f64 (PI.f64) 4)) f) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))

Outputs

(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (*.f64 -2 (fma.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) 1/2) (fma.f64 1/16 (*.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0) (PI.f64)) (*.f64 f f) 0)))

Results

6.0ms	1.3b	`f`
3.0ms	1.3b	`(neg.f64 (.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f))))))))`
3.0ms	1.3b	`(.f64 (/.f64 1 (/.f64 (PI.f64) 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) 4) f)))))))`
4.0ms	1.3b	`(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))))`
3.0ms	1.3b	`(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))))`
6.0ms	1.3b	`(*.f64 (/.f64 (PI.f64) 4) f)`

Compiler

Compiled 409 to 312 computations (23.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	70
1	41	70
2	45	70
3	47	70
4	48	70

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (*.f64 -2 (fma.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) 1/2) (fma.f64 1/16 (*.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0) (PI.f64)) (*.f64 f f) 0)))

Outputs

(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (*.f64 -2 (fma.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) 1/2) (fma.f64 1/16 (*.f64 1 (/.f64 (PI.f64) 1/2)) (*.f64 (*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48) -2)) 0) (PI.f64)) (*.f64 f f) 0)))

(fma.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 2 (*.f64 (PI.f64) 1/2))) (log.f64 f)) (PI.f64)) (*.f64 -2 (fma.f64 (/.f64 (fma.f64 (*.f64 (PI.f64) 1/2) (fma.f64 1/16 (/.f64 (PI.f64) 1/2) (*.f64 -2 (*.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (PI.f64) 2)) 1/48))) 0) (PI.f64)) (*.f64 f f) 0)))

end36.0ms (0.2%)

Stop Event

1×

fuel

Compiler

Compiled 88 to 70 computations (20.5% saved)

Details

analyze1.5s (9.9%)

sample11.1s (74.8%)

preprocess30.0ms (0.2%)

simplify24.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series100.0ms (0.7%)

rewrite56.0ms (0.4%)

simplify51.0ms (0.3%)

prune222.0ms (1.5%)

localize32.0ms (0.2%)

series0.0ms (0%)

rewrite75.0ms (0.5%)

simplify12.0ms (0.1%)

prune557.0ms (3.7%)

localize19.0ms (0.1%)

series0.0ms (0%)

rewrite53.0ms (0.4%)

simplify6.0ms (0%)

prune413.0ms (2.8%)

localize21.0ms (0.1%)

series78.0ms (0.5%)

rewrite63.0ms (0.4%)

simplify11.0ms (0.1%)

prune362.0ms (2.4%)

regimes33.0ms (0.2%)

simplify3.0ms (0%)

end36.0ms (0.2%)

Profiling