Details

analyze1.5s (8.7%)

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)

sample401.0ms (2.3%)

Algorithm

1×

intervals

Results

100.0ms	122×	body	1024	valid
77.0ms	124×	body	1024	nan
36.0ms	22×	body	2048	valid
26.0ms	55×	body	512	valid
22.0ms	48×	body	512	nan
12.0ms	35×	body	256	nan
11.0ms	35×	body	256	valid
4.0ms	22×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify63.0ms (0.4%)

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

prune5.0ms (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)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (PI.f64) f)
✓	0.4b	(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)))))
✓	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))))
✓	6.0b	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))

series754.0ms (4.3%)

Counts

4 → 48

Calls

4 calls:

702.0ms	(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)))))
38.0ms	(/.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))))
11.0ms	(-.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)

rewrite62.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
56×	`times-frac_binary64`
47×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`

Counts

4 → 172

Calls

4 calls:

16.0ms	(/.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))))
11.0ms	(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)))))
6.0ms	(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f)))
4.0ms	(*.f64 (PI.f64) f)

simplify510.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
446×	`fma-neg_binary64`
309×	`cancel-sign-sub-inv_binary64`
196×	`unswap-sqr_binary64`
193×	`exp-prod_binary64`

Counts

220 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	339	12804
1	728	11342
2	2171	10169
3	4156	10095
4	5101	10095

prune493.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	292	7	299
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	293	7	300

Error

1.7b

Counts

300 → 7

Alt Table

Status	Error	Program
	61.5b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))) 3)) (/.f64 -4 (PI.f64)))
	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 f (PI.f64)))) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2)) (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4)))))) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (+.f64 (neg.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)))))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (sqrt.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	61.6b	(.f64 (+.f64 (log.f64 (/.f64 (hypot.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) 1/8) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/8)) (+.f64 (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f (PI.f64))) (sqrt.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)))))) (log.f64 (/.f64 (hypot.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) 1/8) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/8)) (-.f64 (sqrt.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	61.7b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	2.5b	(*.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 -4 (PI.f64)))
▶	2.3b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

Compiler

Compiled 15454 to 10016 computations (35.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
✓	0.3b	(*.f64 f (PI.f64))
✓	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	0.4b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))

series42.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

22.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
9.0ms	(/.f64 4 (*.f64 f (PI.f64)))
8.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))
3.0ms	(*.f64 f (PI.f64))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 88

Calls

4 calls:

8.0ms	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))
4.0ms	(/.f64 4 (*.f64 f (PI.f64)))
3.0ms	(*.f64 f (PI.f64))
0.0ms	(fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))

simplify139.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
336×	`fma-neg_binary64`
319×	`associate-/r*_binary64`
281×	`associate-*l/_binary64`
280×	`associate-*r/_binary64`

Counts

112 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	2580
1	546	2310
2	1707	2301
3	4281	2293
4	4990	2293
5	4930	2293

prune270.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	196	7	203
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	197	13	210

Error

1.3b

Counts

210 → 13

Alt Table

Status	Error	Program
	2.5b	(.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (.f64 (sqrt.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (/.f64 -4 (PI.f64))))
	2.5b	(cbrt.f64 (.f64 (.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64)))))) (log.f64 (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)))))
	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 f (PI.f64)))) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2)) (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4)))))) (/.f64 -4 (PI.f64)))
	2.2b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	61.6b	(.f64 (+.f64 (log.f64 (/.f64 (hypot.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) 1/8) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/8)) (+.f64 (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f (PI.f64))) (sqrt.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)))))) (log.f64 (/.f64 (hypot.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) 1/8) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/8)) (-.f64 (sqrt.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
	3.5b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (*.f64 (cbrt.f64 (/.f64 -4 (PI.f64))) (cbrt.f64 (/.f64 -4 (PI.f64))))) (cbrt.f64 (/.f64 -4 (PI.f64))))
▶	2.2b	(.f64 (.f64 (log.f64 (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))))
	61.7b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	62.6b	(log1p.f64 (expm1.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
	2.5b	(*.f64 (-.f64 (log.f64 (/.f64 4 (PI.f64))) (log.f64 f)) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))) 3)) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (+.f64 (neg.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)))))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (sqrt.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	2.4b	(.f64 (/.f64 (log.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f)))) (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64))))

Compiler

Compiled 5383 to 3227 computations (40.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 1 (sqrt.f64 (PI.f64))))
✓	0.3b	(.f64 (.f64 (log.f64 (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))))
	0.3b	(/.f64 4 (*.f64 f (PI.f64)))
✓	1.0b	(sqrt.f64 (PI.f64))

series49.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

25.0ms

(*.f64 (*.f64 (log.f64 (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))))

24.0ms

(*.f64 (log.f64 (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))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log_binary64`
44×	`associate-r_binary64`
44×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`

Counts

3 → 121

Calls

3 calls:

12.0ms

(*.f64 (*.f64 (log.f64 (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))))

10.0ms

(*.f64 (log.f64 (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))

simplify253.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-def_binary64`
397×	`cancel-sign-sub-inv_binary64`
396×	`fma-neg_binary64`
284×	`times-frac_binary64`
260×	`associate-l_binary64`

Counts

145 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	296	5315
1	791	4548
2	2665	4280
3	4517	4270
4	4952	4270
5	5000	4270
6	4908	4270

prune360.0ms (2.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	256	3	259
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	260	12	272

Error

1.3b

Counts

272 → 12

Alt Table

Status	Error	Program
	61.5b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))) 3)) (/.f64 -4 (PI.f64)))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64)))))
	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 f (PI.f64)))) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2)) (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4)))))) (/.f64 -4 (PI.f64)))
	2.2b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	61.6b	(.f64 (+.f64 (log.f64 (/.f64 (hypot.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) 1/8) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/8)) (+.f64 (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f (PI.f64))) (sqrt.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)))))) (log.f64 (/.f64 (hypot.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) 1/8) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/8)) (-.f64 (sqrt.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
▶	2.2b	(.f64 (log.f64 (pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.3b	(/.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
	3.5b	(.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (*.f64 (cbrt.f64 (/.f64 -4 (PI.f64))) (cbrt.f64 (/.f64 -4 (PI.f64))))) (cbrt.f64 (/.f64 -4 (PI.f64))))
✓	2.2b	(.f64 (.f64 (log.f64 (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))))
	61.7b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (+.f64 (neg.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)))))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (sqrt.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	62.6b	(log1p.f64 (expm1.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))

Compiler

Compiled 8471 to 5066 computations (40.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series45.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

37.0ms	(pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))
8.0ms	(/.f64 4 (*.f64 (PI.f64) f))
0.0ms	(*.f64 (PI.f64) 1/12)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 75

Calls

3 calls:

4.0ms	(pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))
3.0ms	(/.f64 4 (*.f64 (PI.f64) f))
3.0ms	(*.f64 (PI.f64) 1/12)

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-def_binary64`
416×	`associate-/r*_binary64`
380×	`times-frac_binary64`
253×	`cancel-sign-sub-inv_binary64`
229×	`associate-/l*_binary64`

Counts

99 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	3112
1	640	2928
2	2002	2583
3	4913	2583

prune226.0ms (1.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	131	12	143

Error

1.3b

Counts

143 → 12

Alt Table

Status	Error	Program
	61.5b	(.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))) 3)) (/.f64 -4 (PI.f64)))
	2.6b	(.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (.f64 f (PI.f64))))) (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 -4 (sqrt.f64 (PI.f64)))))
	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 f (PI.f64)))) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/2)) (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4)))))) (/.f64 -4 (PI.f64)))
	2.2b	(fma.f64 4 (-.f64 (/.f64 (log.f64 f) (PI.f64)) (/.f64 (log.f64 (/.f64 4 (PI.f64))) (PI.f64))) (.f64 (.f64 (PI.f64) (*.f64 f f)) -1/12))
	61.6b	(.f64 (+.f64 (log.f64 (/.f64 (hypot.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) 1/8) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/8)) (+.f64 (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 f (PI.f64))) (sqrt.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)))))) (log.f64 (/.f64 (hypot.f64 (pow.f64 (exp.f64 (.f64 f (PI.f64))) 1/8) (pow.f64 (exp.f64 (.f64 f (PI.f64))) -1/8)) (-.f64 (sqrt.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (*.f64 f (PI.f64))))))) (/.f64 -4 (PI.f64)))
✓	2.2b	(.f64 (log.f64 (pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f))) (sqrt.f64 (/.f64 1 (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64))))
	2.3b	(/.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
✓	2.2b	(.f64 (.f64 (log.f64 (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))))
	61.7b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 (PI.f64) f))) (log.f64 (exp.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	61.5b	(.f64 (+.f64 (neg.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4)))))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (.f64 f (PI.f64)) -1/4))) (sqrt.f64 (-.f64 (exp.f64 (.f64 (.f64 f (PI.f64)) 1/4)) (exp.f64 (.f64 (*.f64 f (PI.f64)) -1/4))))))) (/.f64 -4 (PI.f64)))
	62.6b	(log1p.f64 (expm1.f64 (.f64 (log.f64 (fma.f64 (.f64 f (PI.f64)) 1/12 (/.f64 4 (*.f64 f (PI.f64))))) (/.f64 -4 (PI.f64)))))
	3.8b	(.f64 (log.f64 (pow.f64 (pow.f64 (fma.f64 f (.f64 (PI.f64) 1/12) (/.f64 4 (*.f64 (PI.f64) f))) (fabs.f64 (cbrt.f64 (/.f64 1 (PI.f64))))) (sqrt.f64 (cbrt.f64 (/.f64 1 (PI.f64)))))) (/.f64 -4 (sqrt.f64 (PI.f64))))

Compiler

Compiled 5110 to 3532 computations (30.9% saved)

regimes2.1s (11.7%)

Accuracy

Total 0.7b remaining (34%)

Threshold costs 0.7b (34%)

Counts

216 → 1

Compiler

Compiled 34962 to 25064 computations (28.3% saved)

simplify4.0ms (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

end2.0ms (0%)

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

sample10.1s (57.3%)

Algorithm

1×

intervals

Results

2.8s	3894×	body	1024	valid
2.8s	3852×	body	1024	nan
1.0s	1943×	body	512	nan
995.0ms	1980×	body	512	valid
752.0ms	500×	body	2048	valid
344.0ms	984×	body	256	valid
322.0ms	996×	body	256	nan
117.0ms	642×	body	128	valid
4.0ms	5×	body	2048	nan
0.0ms	2×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 478 to 334 computations (30.1% saved)

Details

analyze1.5s (8.7%)

sample401.0ms (2.3%)

simplify63.0ms (0.4%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series754.0ms (4.3%)

rewrite62.0ms (0.4%)

simplify510.0ms (2.9%)

prune493.0ms (2.8%)

localize11.0ms (0.1%)

series42.0ms (0.2%)

rewrite20.0ms (0.1%)

simplify139.0ms (0.8%)

prune270.0ms (1.5%)

localize13.0ms (0.1%)

series49.0ms (0.3%)

rewrite37.0ms (0.2%)

simplify253.0ms (1.4%)

prune360.0ms (2.1%)

localize18.0ms (0.1%)

series45.0ms (0.3%)

rewrite14.0ms (0.1%)

simplify98.0ms (0.6%)

prune226.0ms (1.3%)

regimes2.1s (11.7%)

simplify4.0ms (0%)

end2.0ms (0%)

sample10.1s (57.3%)

Profiling