Details

analyze1.4s (7.3%)

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)

sample394.0ms (2.1%)

Algorithm

1×

intervals

Results

127.0ms	124×	body	1024	valid
64.0ms	101×	body	1024	nan
41.0ms	65×	body	512	nan
29.0ms	60×	body	512	valid
20.0ms	16×	body	2048	valid
12.0ms	35×	body	256	valid
10.0ms	32×	body	256	nan
4.0ms	21×	body	128	valid

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify48.0ms (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

61.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	61.2b	(.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

▶

61.2b

(*.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
✓	0.3b	(*.f64 (/.f64 (PI.f64) 4) f)
✓	0.3b	(*.f64 (PI.f64) f)
✓	1.2b	(/.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))))
✓	5.1b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series79.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

65.0ms	(/.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)

rewrite41.0ms (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:

13.0ms	(/.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)))
5.0ms	(*.f64 (/.f64 (PI.f64) 4) f)
3.0ms	(*.f64 (PI.f64) f)

simplify304.0ms (1.6%)

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

prune471.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	344	5	349
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	345	5	350

Error

2.0b

Counts

350 → 5

Alt Table

Status	Error	Program
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))
▶	2.1b	(.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)))
	2.3b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.6b	(.f64 (log.f64 (/.f64 4 (.f64 f (PI.f64)))) (/.f64 -4 (PI.f64)))
	61.2b	(.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)) (.f64 (neg.f64 (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 16122 to 10458 computations (35.1% saved)

localize38.0ms (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)
✓	1.2b	(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)

series407.0ms (2.2%)

Counts

4 → 24

Calls

4 calls:

216.0ms	(.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)))
191.0ms	(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:

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)))
2.0ms	(pow.f64 (PI.f64) 7)
1.0ms	(pow.f64 (PI.f64) 5)

simplify237.0ms (1.3%)

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

prune537.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	190	9	199

Error

1.7b

Counts

199 → 9

Alt Table

Status	Error	Program
	2.4b	(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))))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))
	2.1b	(.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))))
▶	2.1b	(.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)))
	2.3b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.3b	(.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))))
	2.5b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	61.2b	(.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)) (.f64 (neg.f64 (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
	3.0b	(.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)))))

Compiler

Compiled 19499 to 13132 computations (32.7% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(pow.f64 (PI.f64) 5)
✓	1.2b	(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))))))))
	1.6b	(pow.f64 (PI.f64) 7)
✓	2.2b	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 -1/4 (.f64 (PI.f64) f))) (exp.f64 (*.f64 f (/.f64 (PI.f64) 4))))))

series436.0ms (2.4%)

Counts

2 → 24

Calls

2 calls:

373.0ms

(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))))))))

rewrite20.0ms (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))))))))

5.0ms

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

simplify143.0ms (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

prune537.0ms (2.9%)

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

1.7b

Counts

174 → 9

Alt Table

Status	Error	Program
	2.4b	(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))))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))
▶	2.1b	(.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))))
✓	2.1b	(.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)))
	2.3b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.3b	(.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))))
	2.5b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	61.2b	(.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)) (.f64 (neg.f64 (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
	3.0b	(.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)))))

Compiler

Compiled 14700 to 10278 computations (30.1% saved)

localize36.0ms (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))
	1.2b	(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))

simplify130.0ms (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

prune430.0ms (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

1.7b

Counts

153 → 9

Alt Table

Status	Error	Program
	2.4b	(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))))
	61.2b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) 3) (pow.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)) 3)) (+.f64 (sqrt.f64 (exp.f64 (.f64 f (PI.f64)))) (+.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2) (pow.f64 (exp.f64 f) (+.f64 (.f64 -1/4 (PI.f64)) (*.f64 1/4 (PI.f64))))))))) (/.f64 -4 (PI.f64)))
✓	2.1b	(.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))))
✓	2.1b	(.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)))
	2.3b	(.f64 (log.f64 (+.f64 (.f64 4 (/.f64 1 (.f64 f (PI.f64)))) (.f64 1/12 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	2.3b	(.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))))
	2.5b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	61.2b	(.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)) (.f64 (neg.f64 (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 (PI.f64) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 (PI.f64) f)))))) (/.f64 -4 (PI.f64)))
	3.0b	(.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)))))

Compiler

Compiled 13211 to 8757 computations (33.7% saved)

regimes3.5s (19%)

Accuracy

Total 0.6b remaining (28.6%)

Threshold costs 0.6b (28.6%)

Counts

290 → 1

Compiler

Compiled 86280 to 63266 computations (26.7% 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

end1.0ms (0%)

Compiler: Compiled 50 to 36 computations (28% saved)

sample9.2s (50%)

Algorithm

1×

intervals

Results

2.7s	3964×	body	1024	valid
2.4s	3774×	body	1024	nan
956.0ms	1934×	body	512	valid
916.0ms	1931×	body	512	nan
680.0ms	493×	body	2048	valid
316.0ms	993×	body	256	valid
288.0ms	946×	body	256	nan
104.0ms	616×	body	128	valid
1.0ms	1×	body	2048	nan
1.0ms	4×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 654 to 473 computations (27.7% saved)

Details

analyze1.4s (7.3%)

sample394.0ms (2.1%)

simplify48.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series79.0ms (0.4%)

rewrite41.0ms (0.2%)

simplify304.0ms (1.6%)

prune471.0ms (2.5%)

localize38.0ms (0.2%)

series407.0ms (2.2%)

rewrite25.0ms (0.1%)

simplify237.0ms (1.3%)

prune537.0ms (2.9%)

localize37.0ms (0.2%)

series436.0ms (2.4%)

rewrite20.0ms (0.1%)

simplify143.0ms (0.8%)

prune537.0ms (2.9%)

localize36.0ms (0.2%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify130.0ms (0.7%)

prune430.0ms (2.3%)

regimes3.5s (19%)

simplify3.0ms (0%)

end1.0ms (0%)

sample9.2s (50%)

Profiling