Details

analyze2.9s (15.4%)

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)

sample656.0ms (3.5%)

Algorithm

1×

intervals

Results

202.0ms	121×	body	1024	nan
163.0ms	118×	body	1024	valid
111.0ms	66×	body	512	nan
64.0ms	67×	body	512	valid
47.0ms	20×	body	2048	valid
19.0ms	29×	body	256	valid
15.0ms	26×	body	256	nan
7.0ms	22×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify58.0ms (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

60.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (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

▶

60.6b

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

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	0.2b	(*.f64 (PI.f64) f)
✓	0.8b	(/.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))))
✓	5.5b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series97.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

69.0ms	(/.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))))
18.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
6.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
5.0ms	(*.f64 (PI.f64) f)

rewrite75.0ms (0.4%)

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:

19.0ms	(/.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))))
12.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
8.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
5.0ms	(*.f64 (PI.f64) f)

simplify410.0ms (2.2%)

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

prune638.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	347	2	349
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	347	3	350

Error

1.1b

Counts

350 → 3

Alt Table

Status	Error	Program
▶	1.7b	(.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 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
✓	60.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 15919 to 10312 computations (35.2% saved)

localize69.0ms (0.4%)

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)))
✓	0.7b	(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))))))))
✓	1.0b	(pow.f64 (PI.f64) 5)
✓	1.6b	(pow.f64 (PI.f64) 7)

series748.0ms (4%)

Counts

4 → 24

Calls

4 calls:

459.0ms	(.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)))
288.0ms	(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)

rewrite54.0ms (0.3%)

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:

11.0ms	(.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)))
11.0ms	(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))))))))
3.0ms	(pow.f64 (PI.f64) 7)
3.0ms	(pow.f64 (PI.f64) 5)

simplify212.0ms (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

prune481.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	185	9	194
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	186	11	197

Error

0.8b

Counts

197 → 11

Alt Table

Status	Error	Program
▶	1.6b	(/.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)))))))) -4) (PI.f64))
	1.7b	(.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)))
	1.9b	(-.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)))))
	2.0b	(.f64 (.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))))))))) (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)))
	1.8b	(.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))))
	1.7b	(.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))))
	1.8b	(.f64 (+.f64 (neg.f64 (log.f64 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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)))))))))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))) (cbrt.f64 (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	(cbrt.f64 (.f64 (pow.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)))))))) 3) (/.f64 -64 (pow.f64 (PI.f64) 3))))
	2.0b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.6b	(.f64 (.f64 (cbrt.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 -4 (PI.f64)))) (cbrt.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 -4 (PI.f64))))) (cbrt.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 -4 (PI.f64)))))
✓	60.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 19800 to 13348 computations (32.6% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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)))))))) -4) (PI.f64))
	0.7b	(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))))))))
	1.0b	(pow.f64 (PI.f64) 5)
	1.6b	(pow.f64 (PI.f64) 7)

series197.0ms (1.1%)

Counts

1 → 12

Calls

1 calls:

197.0ms

(/.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)))))))) -4) (PI.f64))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/r*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 23

Calls

1 calls:

9.0ms

(/.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)))))))) -4) (PI.f64))

simplify143.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

311×	`unswap-sqr_binary64`
217×	`cancel-sign-sub-inv_binary64`
200×	`fma-neg_binary64`
187×	`sub-neg_binary64`
177×	`times-frac_binary64`

Counts

35 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	5656
1	781	5101
2	3324	4967
3	4973	4967
4	4951	4967

prune479.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	175	9	184

Error

0.8b

Counts

184 → 9

Alt Table

Status	Error	Program
	1.7b	(/.f64 1 (/.f64 (PI.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)))))))) -4)))
	1.9b	(-.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)))))
	1.7b	(/.f64 (.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4))))) (log.f64 (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) (PI.f64))
	2.0b	(/.f64 (.f64 (cbrt.f64 (pow.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)))))))) 3)) -4) (PI.f64))
✓	60.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
	1.7b	(.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))))
▶	1.7b	(.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	(cbrt.f64 (.f64 (pow.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)))))))) 3) (/.f64 -64 (pow.f64 (PI.f64) 3))))
	2.0b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 17418 to 11690 computations (32.9% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(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)
✓	1.7b	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (*.f64 f (/.f64 (PI.f64) 4))))))

series451.0ms (2.4%)

Counts

2 → 24

Calls

2 calls:

379.0ms

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

72.0ms

(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))))))))

rewrite19.0ms (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))))))

simplify135.0ms (0.7%)

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 (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	165	9	174

Error

0.8b

Counts

174 → 9

Alt Table

Status	Error	Program
	1.7b	(/.f64 1 (/.f64 (PI.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)))))))) -4)))
	1.9b	(-.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)))))
	2.4b	(.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (-.f64 (log.f64 (*.f64 2 (/.f64 (sqrt.f64 2) (PI.f64)))) (log.f64 f))) (/.f64 -4 (PI.f64)))
	1.7b	(.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))))
	1.7b	(/.f64 (.f64 (-.f64 (log.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4))))) (log.f64 (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) (PI.f64))
	2.0b	(/.f64 (.f64 (cbrt.f64 (pow.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)))))))) 3)) -4) (PI.f64))
✓	60.6b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64)))
✓	1.7b	(.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 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 14030 to 9804 computations (30.1% saved)

regimes1.2s (6.6%)

Accuracy

Total 0.6b remaining (32.2%)

Threshold costs 0.6b (32.2%)

Counts

114 → 1

Compiler

Compiled 38016 to 28040 computations (26.2% 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	38	87
1	44	87
2	44	87

end1.0ms (0%)

Compiler: Compiled 54 to 40 computations (25.9% saved)

sample9.0s (48.3%)

Algorithm

1×

intervals

Results

2.6s	3902×	body	1024	valid
2.5s	3903×	body	1024	nan
949.0ms	2017×	body	512	valid
863.0ms	1917×	body	512	nan
637.0ms	486×	body	2048	valid
312.0ms	967×	body	256	valid
285.0ms	965×	body	256	nan
112.0ms	628×	body	128	valid
1.0ms	4×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 485 to 360 computations (25.8% saved)

Details

analyze2.9s (15.4%)

sample656.0ms (3.5%)

simplify58.0ms (0.3%)

prune8.0ms (0%)

localize34.0ms (0.2%)

series97.0ms (0.5%)

rewrite75.0ms (0.4%)

simplify410.0ms (2.2%)

prune638.0ms (3.4%)

localize69.0ms (0.4%)

series748.0ms (4%)

rewrite54.0ms (0.3%)

simplify212.0ms (1.1%)

prune481.0ms (2.6%)

localize32.0ms (0.2%)

series197.0ms (1.1%)

rewrite11.0ms (0.1%)

simplify143.0ms (0.8%)

prune479.0ms (2.6%)

localize33.0ms (0.2%)

series451.0ms (2.4%)

rewrite19.0ms (0.1%)

simplify135.0ms (0.7%)

prune473.0ms (2.5%)

regimes1.2s (6.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample9.0s (48.3%)

Profiling