Details

analyze1.3s (8.4%)

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)

sample11.3s (72.4%)

Results

3.5s	4038×	body	1024	valid
3.2s	4037×	body	1024	invalid
1.3s	2114×	body	512	invalid
1.3s	1992×	body	512	valid
890.0ms	514×	body	2048	valid
542.0ms	1062×	body	256	valid
400.0ms	1047×	body	256	invalid
149.0ms	650×	body	128	valid
1.0ms	1×	body	2048	invalid
1.0ms	3×	body	128	invalid

Compiler

Compiled 116 to 92 computations (20.7% saved)

simplify49.0ms (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

60.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.8b	(.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

▶

60.8b

(*.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))))
✓	5.4b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series45.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

31.0ms	(/.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 (PI.f64) f)
3.0ms	(*.f64 (/.f64 (PI.f64) 4) f)

rewrite36.0ms (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:

9.0ms	(/.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 (/.f64 (PI.f64) 4) f)
5.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
2.0ms	(*.f64 (PI.f64) f)

simplify203.0ms (1.3%)

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

prune307.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	346	3	349
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	347	3	350

Error

1.4b

Counts

350 → 3

Alt Table

Status	Error	Program
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (exp.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
▶	1.8b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	2.1b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 15920 to 10310 computations (35.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 f (PI.f64)) 3)
✓	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.5b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
✓	1.0b	(pow.f64 (PI.f64) 5)

series46.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

32.0ms	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
7.0ms	(pow.f64 (*.f64 f (PI.f64)) 3)
6.0ms	(/.f64 4 (*.f64 f (PI.f64)))
0.0ms	(pow.f64 (PI.f64) 5)

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

4 → 101

Calls

4 calls:

6.0ms	(/.f64 4 (*.f64 f (PI.f64)))
6.0ms	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
2.0ms	(pow.f64 (*.f64 f (PI.f64)) 3)
2.0ms	(pow.f64 (PI.f64) 5)

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

344×	`times-frac_binary64`
328×	`associate-/l*_binary64`
315×	`fma-neg_binary64`
303×	`fma-def_binary64`
220×	`unswap-sqr_binary64`

Counts

125 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	257	3602
1	614	3215
2	2100	3188
3	4931	3183
4	5033	3183

prune267.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	165	7	172
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	166	9	175

Error

1.0b

Counts

175 → 9

Alt Table

Status	Error	Program
	2.5b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
▶	1.8b	(.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.1b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	2.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))))) (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	2.1b	(cbrt.f64 (.f64 (.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (*.f64 (/.f64 -4 (PI.f64)) (/.f64 -4 (PI.f64))) (/.f64 -4 (PI.f64)))))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (exp.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	13.8b	(log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	2.1b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
	1.9b	(fma.f64 7/5760 (.f64 (pow.f64 f 4) (pow.f64 (PI.f64) 3)) (fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (PI.f64) (.f64 (.f64 f f) -1/12))))

Compiler

Compiled 7497 to 4837 computations (35.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.3b	(.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64))))
✓	1.0b	(sqrt.f64 (PI.f64))
	1.0b	(pow.f64 (PI.f64) 5)

series32.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

31.0ms

(*.f64 (log.f64 (fma.f64 (pow.f64 (*.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (*.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64))))

0.0ms

(sqrt.f64 (PI.f64))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
22×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

8.0ms

(*.f64 (log.f64 (fma.f64 (pow.f64 (*.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (*.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (*.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))))) (/.f64 1 (sqrt.f64 (PI.f64))))

1.0ms

(sqrt.f64 (PI.f64))

simplify134.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

931×	`fma-neg_binary64`
555×	`times-frac_binary64`
362×	`fma-def_binary64`
339×	`associate-l_binary64`
289×	`cancel-sign-sub-inv_binary64`

Counts

77 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	3929
1	444	3523
2	1203	3454
3	3246	3446
4	4850	3446
5	5160	3446

prune274.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	181	9	190

Error

1.0b

Counts

190 → 9

Alt Table

Status	Error	Program
▶	1.7b	(.f64 (log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 (.f64 (PI.f64) f) 1/12 (/.f64 4 (*.f64 (PI.f64) f))))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.1b	(cbrt.f64 (.f64 (.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (*.f64 (/.f64 -4 (PI.f64)) (/.f64 -4 (PI.f64))) (/.f64 -4 (PI.f64)))))
	2.5b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	2.1b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	2.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))))) (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (exp.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	13.8b	(log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	2.1b	(.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 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (cbrt.f64 (pow.f64 (PI.f64) 3/2)))) (/.f64 -4 (sqrt.f64 (PI.f64))))

Compiler

Compiled 9052 to 5684 computations (37.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 4 (*.f64 (PI.f64) f))
	1.0b	(sqrt.f64 (PI.f64))
	1.0b	(pow.f64 (PI.f64) 5)
✓	3.8b	(pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 (.f64 (PI.f64) f) 1/12 (/.f64 4 (.f64 (PI.f64) f))))) (sqrt.f64 (/.f64 1 (PI.f64))))

series51.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

43.0ms

(pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 (*.f64 (PI.f64) f) 1/12 (/.f64 4 (*.f64 (PI.f64) f))))) (sqrt.f64 (/.f64 1 (PI.f64))))

9.0ms

(/.f64 4 (*.f64 (PI.f64) f))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow-unpow_binary64`
13×	`sqrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

3.0ms

(/.f64 4 (*.f64 (PI.f64) f))

3.0ms

(pow.f64 (fma.f64 (pow.f64 (*.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 (*.f64 (PI.f64) f) 1/12 (/.f64 4 (*.f64 (PI.f64) f))))) (sqrt.f64 (/.f64 1 (PI.f64))))

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
379×	`associate-/r*_binary64`
319×	`times-frac_binary64`
279×	`cancel-sign-sub-inv_binary64`
216×	`associate-/l*_binary64`

Counts

79 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	4042
1	627	3851
2	1914	3464
3	4950	3464

prune233.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	131	9	140

Error

1.0b

Counts

140 → 9

Alt Table

Status	Error	Program
✓	1.7b	(.f64 (log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 (.f64 (PI.f64) f) 1/12 (/.f64 4 (*.f64 (PI.f64) f))))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.1b	(cbrt.f64 (.f64 (.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (*.f64 (/.f64 -4 (PI.f64)) (/.f64 -4 (PI.f64))) (/.f64 -4 (PI.f64)))))
	2.5b	(*.f64 -4 (/.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (PI.f64)))
	2.1b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	2.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))))) (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))))) (.f64 (cbrt.f64 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64)))))))) (/.f64 -4 (PI.f64))))
	60.8b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (exp.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 (PI.f64) f))))))) (/.f64 -4 (PI.f64)))
	13.8b	(log.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (PI.f64) f) 3) -1/2880 (fma.f64 1/483840 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 f 5)) (fma.f64 1/12 (.f64 (PI.f64) f) (/.f64 4 (.f64 (PI.f64) f))))) (/.f64 -4 (PI.f64))))
	2.1b	(.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 (log.f64 (fma.f64 (pow.f64 (.f64 f (PI.f64)) 3) -1/2880 (fma.f64 (.f64 (pow.f64 f 5) (pow.f64 (PI.f64) 5)) 1/483840 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))))) (/.f64 1 (cbrt.f64 (pow.f64 (PI.f64) 3/2)))) (/.f64 -4 (sqrt.f64 (PI.f64))))

Compiler

Compiled 7191 to 4925 computations (31.5% saved)

regimes678.0ms (4.3%)

Accuracy

Total 0.5b remaining (26.2%)

Threshold costs 0.5b (26.2%)

Counts

86 → 1

Compiler

Compiled 19776 to 14108 computations (28.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	65
1	34	65
2	33	65

end316.0ms (2%)

Compiler: Compiled 503 to 346 computations (31.2% saved)

Details

analyze1.3s (8.4%)

sample11.3s (72.4%)

simplify49.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series45.0ms (0.3%)

rewrite36.0ms (0.2%)

simplify203.0ms (1.3%)

prune307.0ms (2%)

localize18.0ms (0.1%)

series46.0ms (0.3%)

rewrite20.0ms (0.1%)

simplify108.0ms (0.7%)

prune267.0ms (1.7%)

localize20.0ms (0.1%)

series32.0ms (0.2%)

rewrite17.0ms (0.1%)

simplify134.0ms (0.9%)

prune274.0ms (1.8%)

localize24.0ms (0.2%)

series51.0ms (0.3%)

rewrite9.0ms (0.1%)

simplify88.0ms (0.6%)

prune233.0ms (1.5%)

regimes678.0ms (4.3%)

simplify2.0ms (0%)

end316.0ms (2%)

Profiling