Details

analyze2.8s (13.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0%	98.1%	1.9%	13
0%	98.1%	1.9%	14

Compiler

Compiled 59 to 22 computations (62.7% saved)

sample9.4s (47.1%)

Results

3.3s	16357×	body	128	invalid
2.3s	2243×	body	4096	valid
1.4s	1151×	body	8192	valid
1.1s	1317×	body	2048	valid
505.0ms	2489×	body	128	valid
400.0ms	599×	body	1024	valid
152.0ms	308×	body	512	valid
55.0ms	149×	body	256	valid
46.0ms	58×	body	2048	invalid
36.0ms	59×	body	1024	invalid
27.0ms	47×	body	512	invalid
16.0ms	18×	body	4096	invalid
10.0ms	9×	body	8192	exit
6.0ms	19×	body	256	invalid

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
518×	`distribute-neg-frac_binary64`
416×	`fma-def_binary64`
304×	`associate-/l*_binary64`
217×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	78
1	64	74
2	296	74
3	3103	67
4	4218	67
5	5365	67

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

58.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 (.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))

Status

Error

Program

▶

58.9b

(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

61.6b

(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 c0 (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 c0 (*.f64 w h)) (*.f64 (*.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (*.f64 w h)))) (*.f64 M M)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.5b	(.f64 (.f64 w h) (*.f64 D D))
✓	15.7b	(sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))
✓	16.7b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	27.5b	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))

series884.0ms (4.4%)

Counts

4 → 240

Calls

4 calls:

326.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))
320.0ms	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))
214.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
23.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite95.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`add-cbrt-cube_binary64`
85×	`add-exp-log_binary64`
47×	`cbrt-unprod_binary64`
47×	`prod-exp_binary64`
17×	`pow1_binary64`

Counts

4 → 108

Calls

4 calls:

39.0ms	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))
26.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))
10.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
5.0ms	(.f64 (.f64 w h) (*.f64 D D))

simplify264.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

845×	`times-frac_binary64`
433×	`fma-neg_binary64`
365×	`associate-/l*_binary64`
362×	`associate-/r*_binary64`
140×	`associate-*l/_binary64`

Counts

348 → 233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	379	15401
1	1066	14410
2	4782	14410
3	5131	14410

prune687.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	407	10	417
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	409	10	419

Error

33.8b

Counts

419 → 10

Alt Table

Status	Error	Program
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (expm1.f64 (log1p.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (pow.f64 d 4) (pow.f64 D 4)) (.f64 (/.f64 c0 (.f64 w h)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))))
	59.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M))) (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))))
	57.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	63.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (log.f64 (.f64 d d))) (+.f64 (log.f64 (.f64 w h)) (+.f64 (log.f64 D) (log.f64 D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))))
	48.7b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
▶	41.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 (.f64 d d) c0) (.f64 (.f64 D D) (.f64 w h))) 3)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 (.f64 w h) D) D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	62.3b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))

Compiler

Compiled 27901 to 6487 computations (76.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.0b	(*.f64 (pow.f64 d 2) c0)
✓	10.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
✓	13.9b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
✓	16.5b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))

series625.0ms (3.1%)

Counts

4 → 144

Calls

4 calls:

295.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
257.0ms	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
59.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
13.0ms	(*.f64 (pow.f64 d 2) c0)

rewrite190.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

1737×	`add-exp-log_binary64`
1266×	`prod-exp_binary64`
388×	`div-exp_binary64`
236×	`add-cbrt-cube_binary64`
201×	`pow-exp_binary64`

Counts

4 → 404

Calls

4 calls:

21.0ms	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
10.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
7.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
4.0ms	(*.f64 (pow.f64 d 2) c0)

simplify309.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

680×	`associate-/l/_binary64`
596×	`times-frac_binary64`
518×	`associate-r_binary64`
429×	`associate-l_binary64`
313×	`associate-*r/_binary64`

Counts

548 → 317

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	398	18958
1	752	15353
2	3292	15353
3	5065	15353

prune653.0ms (3.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	303	14	317
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	306	21	327

Error

24.5b

Counts

327 → 21

Alt Table

Status	Error	Program
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	63.6b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2)))) (log.f64 (.f64 (pow.f64 d 2) c0))))))
	41.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (pow.f64 D 2) (/.f64 (.f64 d d) (/.f64 (.f64 w (.f64 (*.f64 M M) h)) c0)))))
	57.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (log.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (log.f64 (pow.f64 d 2)) (log.f64 c0))))))
	41.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 (pow.f64 D 2) (pow.f64 d 2)) (/.f64 (.f64 w (.f64 h (pow.f64 M 2))) c0))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (expm1.f64 (log1p.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (pow.f64 d 4) (pow.f64 D 4)) (.f64 (/.f64 c0 (.f64 w h)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))))
	59.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M))) (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))))
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2)))) (+.f64 (*.f64 (log.f64 d) 2) (log.f64 c0))))))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 (.f64 w h) D) D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	40.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 d (.f64 d c0)))))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 (sqrt.f64 d) 2) (.f64 (pow.f64 (sqrt.f64 d) 2) c0)))))
	63.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (log.f64 (.f64 d d))) (+.f64 (log.f64 (.f64 w h)) (+.f64 (log.f64 D) (log.f64 D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))))
	62.3b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	40.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (.f64 (pow.f64 D 2) w) (.f64 h (pow.f64 M 2))) (*.f64 (pow.f64 d 2) c0))))
▶	34.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	39.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 D (.f64 D (.f64 w (.f64 h (pow.f64 M 2))))) (.f64 (pow.f64 d 2) c0))))
	48.7b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	61.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2))))) (*.f64 (pow.f64 d 2) c0))))
	39.3b	(log.f64 (pow.f64 (exp.f64 (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (.f64 d d) c0))) (.f64 (/.f64 c0 w) 1/4)))
	61.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2))))) (.f64 (pow.f64 d 2) c0))))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (*.f64 (log.f64 d) 2) (log.f64 c0))))))

Compiler

Compiled 13466 to 8205 computations (39.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	6.7b	(*.f64 (pow.f64 M 2) h)
✓	12.7b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	15.3b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series166.0ms (0.8%)

Counts

3 → 40

Calls

3 calls:

125.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
32.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`add-exp-log_binary64`
87×	`prod-exp_binary64`
42×	`pow-exp_binary64`
42×	`pow-to-exp_binary64`
39×	`div-exp_binary64`

Counts

3 → 133

Calls

3 calls:

8.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
6.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
5.0ms	(*.f64 (pow.f64 M 2) h)

simplify118.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-*l/_binary64`
391×	`associate-/l/_binary64`
373×	`*-commutative_binary64`
370×	`associate-*r/_binary64`
310×	`fma-def_binary64`

Counts

173 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	3095
1	332	2730
2	1361	2677
3	4128	2571
4	4913	2571
5	5086	2571

prune560.0ms (2.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	145	15	160
Fresh	10	10	20
Picked	1	0	1
Done	0	0	0
Total	156	25	181

Error

19.5b

Counts

181 → 25

Alt Table

Status	Error	Program
	45.7b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (expm1.f64 (log1p.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (pow.f64 d 4) (pow.f64 D 4)) (.f64 (/.f64 c0 (.f64 w h)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))))
	35.0b	(.f64 1/4 (.f64 (.f64 D D) (/.f64 (.f64 h (.f64 M M)) (.f64 d d))))
	59.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M))) (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))))
	34.4b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) (.f64 (cbrt.f64 (.f64 d d)) (cbrt.f64 (.f64 d d))))) (cbrt.f64 (pow.f64 d 2))))
	59.0b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
▶	31.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	48.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (*.f64 (pow.f64 M 2) h))) (log.f64 (pow.f64 d 2)))))
	31.7b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (*.f64 (log.f64 d) 2) (log.f64 c0))))))
	33.2b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 (.f64 w h) D) D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 (sqrt.f64 d) 2) (.f64 (pow.f64 (sqrt.f64 d) 2) c0)))))
	63.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (log.f64 (.f64 d d))) (+.f64 (log.f64 (.f64 w h)) (+.f64 (log.f64 D) (log.f64 D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))))
	34.7b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	56.4b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	39.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 D (.f64 D (.f64 w (.f64 h (pow.f64 M 2))))) (.f64 (pow.f64 d 2) c0))))
	32.8b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) 2)) (pow.f64 (cbrt.f64 d) 2)))
	51.5b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	32.5b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	45.7b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 D (.f64 h (*.f64 M M)))) (pow.f64 d 2)))
	57.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (log.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (log.f64 (pow.f64 d 2)) (log.f64 c0))))))
	57.5b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	62.3b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))

Compiler

Compiled 5120 to 3131 computations (38.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.6b	(/.f64 (.f64 h (.f64 M M)) d)
✓	6.7b	(.f64 h (.f64 M M))
✓	8.8b	(/.f64 (*.f64 D D) d)
✓	10.7b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series227.0ms (1.1%)

Counts

4 → 132

Calls

4 calls:

179.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
28.0ms	(/.f64 (.f64 h (.f64 M M)) d)
12.0ms	(/.f64 (*.f64 D D) d)
8.0ms	(.f64 h (.f64 M M))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-cbrt-cube_binary64`
77×	`add-exp-log_binary64`
32×	`cbrt-unprod_binary64`
32×	`prod-exp_binary64`
22×	`cbrt-undiv_binary64`

Counts

4 → 123

Calls

4 calls:

11.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
5.0ms	(/.f64 (.f64 h (.f64 M M)) d)
4.0ms	(.f64 h (.f64 M M))
3.0ms	(/.f64 (*.f64 D D) d)

simplify143.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-/r*_binary64`
534×	`associate-/r/_binary64`
461×	`*-commutative_binary64`
309×	`log-div_binary64`
218×	`log-prod_binary64`

Counts

255 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	4137
1	400	3453
2	1576	3453
3	4069	3451
4	4865	3451
5	5026	3451

prune285.0ms (1.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	151	9	160
Fresh	10	14	24
Picked	1	0	1
Done	0	0	0
Total	162	23	185

Error

17.5b

Counts

185 → 23

Alt Table

Status	Error	Program
	28.2b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d D)) (/.f64 (.f64 h (.f64 M M)) d)))
	39.9b	(.f64 1/4 (.f64 (exp.f64 (log.f64 (/.f64 (.f64 D D) d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	54.5b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (/.f64 (.f64 h (.f64 M M)) d)))
	51.5b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	31.5b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	45.7b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (expm1.f64 (log1p.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (pow.f64 d 4) (pow.f64 D 4)) (.f64 (/.f64 c0 (.f64 w h)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))))
	59.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M))) (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))))
	33.2b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	48.1b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 (.f64 w h) D) D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	28.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	27.5b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d))))
	57.5b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	46.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) d)))
	34.7b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	56.4b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	63.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (log.f64 (.f64 d d))) (+.f64 (log.f64 (.f64 w h)) (+.f64 (log.f64 D) (log.f64 D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))))
	57.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (log.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (log.f64 (pow.f64 d 2)) (log.f64 c0))))))
	59.0b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	31.4b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (.f64 M M) (cbrt.f64 d))))
	62.3b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))

Compiler

Compiled 4355 to 1283 computations (70.5% saved)

regimes2.0s (10.1%)

Accuracy

Total 7.4b remaining (27.5%)

Threshold costs 0b (0%)

Counts

145 → 4

Compiler

Compiled 59879 to 35051 computations (41.5% saved)

bsearch9.0ms (0%)

Compiler: Compiled 58 to 21 computations (63.8% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
7×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	416
1	90	416
2	97	416
3	101	416
4	103	416
5	103	416

end366.0ms (1.8%)

Compiler: Compiled 1370 to 610 computations (55.5% saved)

Details

analyze2.8s (13.9%)

sample9.4s (47.1%)

simplify43.0ms (0.2%)

prune5.0ms (0%)

localize20.0ms (0.1%)

series884.0ms (4.4%)

rewrite95.0ms (0.5%)

simplify264.0ms (1.3%)

prune687.0ms (3.4%)

localize19.0ms (0.1%)

series625.0ms (3.1%)

rewrite190.0ms (0.9%)

simplify309.0ms (1.5%)

prune653.0ms (3.3%)

localize11.0ms (0.1%)

series166.0ms (0.8%)

rewrite30.0ms (0.1%)

simplify118.0ms (0.6%)

prune560.0ms (2.8%)

localize11.0ms (0.1%)

series227.0ms (1.1%)

rewrite36.0ms (0.2%)

simplify143.0ms (0.7%)

prune285.0ms (1.4%)

regimes2.0s (10.1%)

bsearch9.0ms (0%)

simplify11.0ms (0.1%)

end366.0ms (1.8%)

Profiling