Details

analyze1.3s (7.7%)

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)

sample11.2s (64.5%)

Results

3.6s	4031×	body	1024	valid
3.3s	3970×	body	1024	invalid
1.3s	2068×	body	512	valid
1.1s	1953×	body	512	invalid
732.0ms	508×	body	2048	valid
427.0ms	1043×	body	256	invalid
407.0ms	982×	body	256	valid
158.0ms	667×	body	128	valid
2.0ms	8×	body	128	invalid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
569×	`fma-def_binary64`
365×	`div-sub_binary64`
240×	`associate-/r*_binary64`
202×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	295	55
4	736	55
5	1625	55
6	4003	55
7	5053	55

prune8.0ms (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

61.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.5b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Status

Error

Program

▶

61.5b

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

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	0.3b	(*.f64 (PI.f64) f)
✓	1.5b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
✓	7.0b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series46.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

33.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
3.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
2.0ms	(*.f64 (PI.f64) f)

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`
21×	`prod-diff_binary64`

Counts

4 → 159

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))))
5.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
4.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
3.0ms	(*.f64 (PI.f64) f)

simplify206.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
588×	`times-frac_binary64`
366×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
196×	`exp-prod_binary64`

Counts

207 → 258

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	312	8603
1	652	7401
2	1996	6651
3	4169	6609
4	4840	6609

prune305.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	345	4	349
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	346	4	350

Error

1.8b

Counts

350 → 4

Alt Table

Status	Error	Program
	61.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (.f64 (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	2.2b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
▶	1.9b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 16064 to 10420 computations (35.1% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
✓	1.0b	(pow.f64 (PI.f64) 5)
✓	1.5b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
✓	1.6b	(pow.f64 (PI.f64) 7)

series302.0ms (1.7%)

Counts

4 → 24

Calls

4 calls:

182.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
119.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
0.0ms	(pow.f64 (PI.f64) 7)
0.0ms	(pow.f64 (PI.f64) 5)

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
22×	`times-frac_binary64`
16×	`log-prod_binary64`

Counts

4 → 102

Calls

4 calls:

5.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
5.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
1.0ms	(pow.f64 (PI.f64) 7)
1.0ms	(pow.f64 (PI.f64) 5)

simplify187.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

336×	`associate-/r*_binary64`
317×	`fma-def_binary64`
282×	`associate-r_binary64`
282×	`times-frac_binary64`
225×	`associate-l_binary64`

Counts

126 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	482	13755
1	1396	12909
2	4965	12909

prune536.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	187	7	194
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	189	9	198

Error

1.5b

Counts

198 → 9

Alt Table

Status	Error	Program
▶	1.9b	(.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4))))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))))) (/.f64 -4 (PI.f64)))
	2.0b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (*.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7)))))))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	1.9b	(.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.2b	(.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (/.f64 -4 (PI.f64))))
	2.0b	(.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	2.0b	(-.f64 (fma.f64 4 (/.f64 (log.f64 f) (PI.f64)) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3)))) (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (*.f64 f f)))))
	2.2b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	14.8b	(log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))) (/.f64 -4 (PI.f64))))

Compiler

Compiled 19295 to 12992 computations (32.7% saved)

localize51.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4))))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))))
	1.0b	(pow.f64 (PI.f64) 5)
	1.6b	(pow.f64 (PI.f64) 7)
✓	1.9b	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (*.f64 f (/.f64 (PI.f64) 4))))))

series408.0ms (2.4%)

Counts

2 → 24

Calls

2 calls:

346.0ms

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

62.0ms

(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 -1/4 (*.f64 (PI.f64) f))) (exp.f64 (*.f64 f (/.f64 (PI.f64) 4))))) (fma.f64 1/192 (pow.f64 (*.f64 (PI.f64) f) 3) (fma.f64 1/61440 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (*.f64 (PI.f64) f) (*.f64 1/41287680 (*.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`log-prod_binary64`
26×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

5.0ms

(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 -1/4 (*.f64 (PI.f64) f))) (exp.f64 (*.f64 f (/.f64 (PI.f64) 4))))) (fma.f64 1/192 (pow.f64 (*.f64 (PI.f64) f) 3) (fma.f64 1/61440 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (*.f64 (PI.f64) f) (*.f64 1/41287680 (*.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))))

4.0ms

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

simplify137.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
389×	`associate-l_binary64`
349×	`associate-/r*_binary64`
257×	`associate-/l*_binary64`
213×	`times-frac_binary64`

Counts

84 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	7056
1	644	6529
2	1886	6109
3	5010	6109

prune473.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	165	9	174

Error

1.5b

Counts

174 → 9

Alt Table

Status	Error	Program
✓	1.9b	(.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4))))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))))) (/.f64 -4 (PI.f64)))
	2.0b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (*.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7)))))))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
▶	1.9b	(.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.2b	(.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (/.f64 -4 (PI.f64))))
	2.0b	(.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	2.0b	(-.f64 (fma.f64 4 (/.f64 (log.f64 f) (PI.f64)) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3)))) (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (*.f64 f f)))))
	2.2b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	14.8b	(log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))) (/.f64 -4 (PI.f64))))

Compiler

Compiled 14496 to 10138 computations (30.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(pow.f64 (PI.f64) 5)
✓	1.0b	(sqrt.f64 (PI.f64))
	1.5b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))
	1.6b	(pow.f64 (PI.f64) 7)

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(sqrt.f64 (PI.f64))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt.f64 (PI.f64))

simplify129.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

15 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	94
1	25	93
2	28	93
3	32	93
4	37	93
5	46	93
6	66	93
7	119	93
8	294	93
9	599	93
10	601	93
11	731	93
12	885	93
13	1053	93
14	1282	93
15	1583	93
16	1931	93
17	2406	93
18	3024	93
19	3220	93
20	3394	93
21	3508	93
22	3555	93
23	3607	93
24	4485	93
25	4789	93

prune392.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	144	9	153

Error

1.5b

Counts

153 → 9

Alt Table

Status	Error	Program
✓	1.9b	(.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4))))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))))) (/.f64 -4 (PI.f64)))
	2.0b	(.f64 (/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (*.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7)))))))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))
✓	1.9b	(.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (*.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.2b	(.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7))))))))) (/.f64 -4 (PI.f64))))
	2.0b	(.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))) (log.f64 (fma.f64 1/192 (pow.f64 (.f64 f (PI.f64)) 3) (fma.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) (fma.f64 1/2 (.f64 f (PI.f64)) (.f64 1/41287680 (.f64 (pow.f64 f 7) (pow.f64 (PI.f64) 7)))))))) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	2.0b	(-.f64 (fma.f64 4 (/.f64 (log.f64 f) (PI.f64)) (.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3)))) (fma.f64 4 (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64)) (.f64 1/12 (.f64 (PI.f64) (*.f64 f f)))))
	2.2b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	14.8b	(log.f64 (pow.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (fma.f64 1/192 (pow.f64 (.f64 (PI.f64) f) 3) (fma.f64 1/61440 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/2 (.f64 (PI.f64) f) (.f64 1/41287680 (.f64 (pow.f64 (PI.f64) 7) (pow.f64 f 7))))))) (/.f64 -4 (PI.f64))))

Compiler

Compiled 13109 to 8687 computations (33.7% saved)

regimes1.1s (6.2%)

Accuracy

Total 0.6b remaining (30.3%)

Threshold costs 0.6b (30.3%)

Counts

116 → 1

Compiler

Compiled 35550 to 25790 computations (27.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	80
1	42	80
2	42	80

end352.0ms (2%)

Compiler: Compiled 562 to 407 computations (27.6% saved)

Details

analyze1.3s (7.7%)

sample11.2s (64.5%)

simplify46.0ms (0.3%)

prune8.0ms (0%)

localize14.0ms (0.1%)

series46.0ms (0.3%)

rewrite37.0ms (0.2%)

simplify206.0ms (1.2%)

prune305.0ms (1.8%)

localize32.0ms (0.2%)

series302.0ms (1.7%)

rewrite25.0ms (0.1%)

simplify187.0ms (1.1%)

prune536.0ms (3.1%)

localize51.0ms (0.3%)

series408.0ms (2.4%)

rewrite22.0ms (0.1%)

simplify137.0ms (0.8%)

prune473.0ms (2.7%)

localize34.0ms (0.2%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify129.0ms (0.7%)

prune392.0ms (2.3%)

regimes1.1s (6.2%)

simplify3.0ms (0%)

end352.0ms (2%)

Profiling