Details

analyze1.4s (9.3%)

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)

sample365.0ms (2.4%)

Algorithm

1×

intervals

Results

83.0ms	123×	body	1024	valid
62.0ms	105×	body	1024	nan
56.0ms	36×	body	256	valid
29.0ms	59×	body	512	valid
23.0ms	54×	body	512	nan
14.0ms	10×	body	2048	valid
9.0ms	32×	body	256	nan
4.0ms	28×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% 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

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

60.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.2b	(.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

▶

60.2b

(*.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)

localize15.0ms (0.1%)

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)
✓	1.0b	(/.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))))
✓	7.2b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series49.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

35.0ms	(/.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))))
9.0ms	(-.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)

rewrite38.0ms (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:

10.0ms	(/.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))))
6.0ms	(-.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)
3.0ms	(*.f64 (PI.f64) f)

simplify335.0ms (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

prune335.0ms (2.2%)

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

1.8b

Counts

350 → 3

Alt Table

Status	Error	Program
▶	2.4b	(.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)))
✓	60.2b	(.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)))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 15919 to 10312 computations (35.2% 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	(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)

series451.0ms (3%)

Counts

4 → 24

Calls

4 calls:

234.0ms	(.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)))
216.0ms	(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)

rewrite26.0ms (0.2%)

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:

6.0ms	(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))))))))
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)))
1.0ms	(pow.f64 (PI.f64) 7)
1.0ms	(pow.f64 (PI.f64) 5)

simplify270.0ms (1.8%)

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

prune509.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	189	8	197

Error

1.4b

Counts

197 → 8

Alt Table

Status	Error	Program
▶	2.3b	(.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)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.5b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (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)))))) (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)))
	2.5b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.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)))))))))) (log.f64 (cbrt.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)))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.6b	(cbrt.f64 (pow.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)))))))) (/.f64 -4 (PI.f64))) 3))
	3.1b	(.f64 (exp.f64 (log.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)))
✓	60.2b	(.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 19138 to 12878 computations (32.7% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(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)
✓	1.0b	(sqrt.f64 (PI.f64))
	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))

simplify131.0ms (0.9%)

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

prune463.0ms (3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	144	8	152

Error

1.4b

Counts

152 → 8

Alt Table

Status	Error	Program
✓	2.3b	(.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)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.5b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (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)))))) (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)))
	2.5b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.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)))))))))) (log.f64 (cbrt.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)))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.6b	(cbrt.f64 (pow.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)))))))) (/.f64 -4 (PI.f64))) 3))
	3.1b	(.f64 (exp.f64 (log.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)))
✓	60.2b	(.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 13358 to 8867 computations (33.6% saved)

localize36.0ms (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))))))

series445.0ms (2.9%)

Counts

2 → 24

Calls

2 calls:

376.0ms

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

69.0ms

(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:

6.0ms

(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))))))

simplify134.0ms (0.9%)

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

prune417.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	165	8	173

Error

1.4b

Counts

173 → 8

Alt Table

Status	Error	Program
✓	2.3b	(.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)))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.5b	(-.f64 (.f64 4 (/.f64 (log.f64 f) (PI.f64))) (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)))))) (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)))
	2.5b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.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)))))))))) (log.f64 (cbrt.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)))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.7b	(.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (.f64 f (/.f64 (PI.f64) 4)))))) (-.f64 (log.f64 (*.f64 2 (/.f64 (sqrt.f64 2) (PI.f64)))) (log.f64 f))) (/.f64 -4 (PI.f64)))
	3.1b	(.f64 (exp.f64 (log.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)))
✓	60.2b	(.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 14017 to 9792 computations (30.1% saved)

regimes693.0ms (4.5%)

Accuracy

Total 0.7b remaining (31.3%)

Threshold costs 0.7b (31.3%)

Counts

65 → 1

Compiler

Compiled 25062 to 18230 computations (27.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	91
1	49	91
2	48	91

end1.0ms (0%)

Compiler: Compiled 56 to 40 computations (28.6% saved)

sample9.0s (58.8%)

Algorithm

1×

intervals

Results

2.6s	4013×	body	1024	nan
2.5s	3897×	body	1024	valid
903.0ms	1957×	body	512	valid
889.0ms	1955×	body	512	nan
698.0ms	516×	body	2048	valid
314.0ms	989×	body	256	valid
288.0ms	976×	body	256	nan
106.0ms	641×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	2×	body	128	overflowed
0.0ms	1×	body	128	nan

Compiler

Compiled 474 to 348 computations (26.6% saved)

Details

analyze1.4s (9.3%)

sample365.0ms (2.4%)

simplify46.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series49.0ms (0.3%)

rewrite38.0ms (0.2%)

simplify335.0ms (2.2%)

prune335.0ms (2.2%)

localize32.0ms (0.2%)

series451.0ms (3%)

rewrite26.0ms (0.2%)

simplify270.0ms (1.8%)

prune509.0ms (3.3%)

localize36.0ms (0.2%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify131.0ms (0.9%)

prune463.0ms (3%)

localize36.0ms (0.2%)

series445.0ms (2.9%)

rewrite22.0ms (0.1%)

simplify134.0ms (0.9%)

prune417.0ms (2.7%)

regimes693.0ms (4.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample9.0s (58.8%)

Profiling