Details

analyze2.6s (12.3%)

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)

sample9.6s (45.2%)

Results

3.3s	16448×	body	128	invalid
2.3s	2259×	body	4096	valid
1.5s	1192×	body	8192	valid
1.1s	1388×	body	2048	valid
511.0ms	2345×	body	128	valid
418.0ms	629×	body	1024	valid
152.0ms	315×	body	512	valid
45.0ms	55×	body	2048	invalid
40.0ms	128×	body	256	valid
33.0ms	46×	body	1024	invalid
15.0ms	34×	body	512	invalid
13.0ms	15×	body	4096	invalid
5.0ms	16×	body	256	invalid
2.0ms	2×	body	8192	exit

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify41.0ms (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

prune4.0ms (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

58.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.7b	(.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)))))
▶	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)))))

Status

Error

Program

62.7b

(*.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)))))

▶

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)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.0b	(.f64 (.f64 w h) (*.f64 D D))
✓	12.6b	(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)))
✓	32.0b	(+.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))))

series807.0ms (3.8%)

Counts

4 → 240

Calls

4 calls:

301.0ms	(+.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))))
283.0ms	(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)))
198.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
24.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite102.0ms (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:

45.0ms	(+.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))))
27.0ms	(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)))
11.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
5.0ms	(.f64 (.f64 w h) (*.f64 D D))

simplify255.0ms (1.2%)

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

prune495.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	412	5	417
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	413	6	419

Error

33.0b

Counts

419 → 6

Alt Table

Status	Error	Program
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (sqrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (sqrt.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)))))
	48.8b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	62.7b	(.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)))))
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))))) (cbrt.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)))))
▶	37.7b	(.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))))
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))

Compiler

Compiled 27427 to 6279 computations (77.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.9b	(*.f64 h (pow.f64 M 2))
✓	10.6b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
✓	11.2b	(.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 d 2) c0))))
✓	14.7b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))

series598.0ms (2.8%)

Counts

4 → 156

Calls

4 calls:

274.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
253.0ms	(.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))))
62.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
9.0ms	(*.f64 h (pow.f64 M 2))

rewrite199.0ms (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 h (pow.f64 M 2))

simplify369.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

650×	`associate-/l/_binary64`
565×	`times-frac_binary64`
528×	`associate-r_binary64`
431×	`associate-l_binary64`
313×	`associate-*r/_binary64`

Counts

560 → 317

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	402	19041
1	756	15436
2	3222	15431
3	4966	15431
4	5009	15431

prune659.0ms (3.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	303	14	317
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	305	18	323

Error

25.8b

Counts

323 → 18

Alt Table

Status	Error	Program
	63.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (log.f64 (pow.f64 M 2))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	36.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 (.f64 h (pow.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) 2)) (pow.f64 (cbrt.f64 M) 2)))) (*.f64 (pow.f64 d 2) c0))))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (sqrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (sqrt.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)))))
	48.8b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
▶	32.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	62.7b	(.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)))))
	37.1b	(.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))))
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))))) (cbrt.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)))))
	35.7b	(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)))
	56.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (-.f64 (log.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (*.f64 (log.f64 d) 2) (log.f64 c0))))))
	34.7b	(.f64 c0 (.f64 (/.f64 1/4 w) (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (*.f64 d d) c0))))
	36.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 (.f64 h M) M))) (.f64 (pow.f64 d 2) c0))))
	64.0b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.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)))) (+.f64 (.f64 (log.f64 d) 2) (log.f64 c0))))))
	59.6b	(.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))))
	37.7b	(.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)))))
	37.7b	(.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))))
	60.9b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 w (.f64 h (pow.f64 M 2))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	61.7b	(.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 13098 to 8031 computations (38.7% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
✓	8.9b	(*.f64 (pow.f64 M 2) h)
✓	13.5b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	15.9b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series312.0ms (1.5%)

Counts

4 → 72

Calls

4 calls:

145.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
127.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
31.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite53.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

290×	`add-exp-log_binary64`
190×	`prod-exp_binary64`
78×	`div-exp_binary64`
76×	`pow-exp_binary64`
76×	`pow-to-exp_binary64`

Counts

4 → 205

Calls

4 calls:

12.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
8.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
5.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
4.0ms	(*.f64 (pow.f64 M 2) h)

simplify144.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

506×	`*-commutative_binary64`
444×	`associate-/l/_binary64`
380×	`fma-def_binary64`
373×	`associate-/r/_binary64`
294×	`log-prod_binary64`

Counts

277 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	5669
1	422	5071
2	1672	5018
3	3936	4789
4	5006	4789

prune495.0ms (2.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	215	16	231
Fresh	9	8	17
Picked	1	0	1
Done	0	0	0
Total	225	24	249

Error

17.9b

Counts

249 → 24

Alt Table

Status	Error	Program
	31.7b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 (pow.f64 d 2) (.f64 (pow.f64 M 2) h))))
	49.1b	(.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)))))
	30.6b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (sqrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (sqrt.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)))))
	47.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 D (.f64 h (*.f64 M M)))) (pow.f64 d 2)))
	62.7b	(.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)))))
	53.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))))) (cbrt.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)))))
	60.9b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 w (.f64 h (pow.f64 M 2))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	32.4b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	29.9b	(.f64 1/4 (.f64 (/.f64 (pow.f64 D 2) (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) 2)) (/.f64 (.f64 (pow.f64 M 2) h) (pow.f64 (cbrt.f64 d) 2))))
	56.0b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (.f64 (log.f64 d) 2))))
	49.1b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	42.9b	(.f64 (.f64 1/4 (/.f64 (.f64 D D) d)) (/.f64 (.f64 (pow.f64 M 2) h) (pow.f64 (sqrt.f64 d) 2)))
	55.8b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 (pow.f64 M 2) h))) (*.f64 (log.f64 d) 2))))
	30.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	61.7b	(.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))))))
	54.0b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	36.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 (.f64 h M) M))) (.f64 (pow.f64 d 2) c0))))
	52.9b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	36.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 (.f64 h (pow.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) 2)) (pow.f64 (cbrt.f64 M) 2)))) (*.f64 (pow.f64 d 2) c0))))
▶	28.4b	(.f64 (.f64 1/4 (/.f64 (pow.f64 D 2) d)) (/.f64 (*.f64 (pow.f64 M 2) h) d))
	30.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) 2) (*.f64 (pow.f64 (cbrt.f64 M) 2) h))) (pow.f64 d 2)))
	35.7b	(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)))

Compiler

Compiled 6550 to 4094 computations (37.5% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.3b	(/.f64 (*.f64 (pow.f64 M 2) h) d)
✓	6.7b	(/.f64 (pow.f64 D 2) d)
	8.9b	(*.f64 (pow.f64 M 2) h)
✓	9.3b	(.f64 (.f64 1/4 (/.f64 (pow.f64 D 2) d)) (/.f64 (*.f64 (pow.f64 M 2) h) d))

series187.0ms (0.9%)

Counts

3 → 68

Calls

3 calls:

148.0ms	(.f64 (.f64 1/4 (/.f64 (pow.f64 D 2) d)) (/.f64 (*.f64 (pow.f64 M 2) h) d))
26.0ms	(/.f64 (*.f64 (pow.f64 M 2) h) d)
12.0ms	(/.f64 (pow.f64 D 2) d)

rewrite31.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-exp-log_binary64`
63×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
42×	`div-exp_binary64`
30×	`times-frac_binary64`

Counts

3 → 133

Calls

3 calls:

9.0ms	(.f64 (.f64 1/4 (/.f64 (pow.f64 D 2) d)) (/.f64 (*.f64 (pow.f64 M 2) h) d))
4.0ms	(/.f64 (*.f64 (pow.f64 M 2) h) d)
3.0ms	(/.f64 (pow.f64 D 2) d)

simplify240.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

539×	`associate-/r*_binary64`
515×	`*-commutative_binary64`
440×	`associate-/l/_binary64`
362×	`associate-/r/_binary64`
281×	`log-div_binary64`

Counts

201 → 184

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	206	4166
1	432	3504
2	1619	3504
3	4168	3504
4	4996	3504
5	5002	3504

prune634.0ms (3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	221	9	230
Fresh	9	14	23
Picked	1	0	1
Done	0	0	0
Total	231	23	254

Error

15.6b

Counts

254 → 23

Alt Table

Status	Error	Program
	30.6b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (sqrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (sqrt.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)))))
	62.7b	(.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)))))
	53.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))))) (cbrt.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)))))
	30.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) 2) (*.f64 (pow.f64 (cbrt.f64 M) 2) h))) (pow.f64 d 2)))
	28.1b	(.f64 (.f64 1/4 (/.f64 (pow.f64 D 2) d)) (.f64 (.f64 M M) (/.f64 h d)))
	35.7b	(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)))
	41.9b	(.f64 (.f64 1/4 (/.f64 (.f64 (/.f64 D (sqrt.f64 d)) D) (sqrt.f64 d))) (/.f64 (.f64 (pow.f64 M 2) h) d))
	27.5b	(.f64 (.f64 1/4 (.f64 (/.f64 1 (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) D))) (/.f64 (.f64 (pow.f64 M 2) h) d))
	60.9b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 w (.f64 h (pow.f64 M 2))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	26.2b	(.f64 (.f64 1/4 (.f64 D (/.f64 D d))) (/.f64 (.f64 (pow.f64 M 2) h) d))
	56.0b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (.f64 (log.f64 d) 2))))
	49.1b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	55.8b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 (pow.f64 M 2) h))) (*.f64 (log.f64 d) 2))))
	27.4b	(.f64 (.f64 (.f64 M M) (.f64 1/4 (/.f64 (*.f64 D D) d))) (/.f64 h d))
	54.0b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	52.9b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	26.3b	(.f64 (.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 D (cbrt.f64 d)))) (/.f64 (*.f64 (pow.f64 M 2) h) d))
	47.1b	(.f64 (.f64 1/4 (/.f64 (pow.f64 D 2) d)) (exp.f64 (-.f64 (log.f64 (*.f64 (pow.f64 M 2) h)) (log.f64 d))))
	36.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 (.f64 h (pow.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) 2)) (pow.f64 (cbrt.f64 M) 2)))) (*.f64 (pow.f64 d 2) c0))))
	26.4b	(.f64 (.f64 1/4 (/.f64 (pow.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) 2) (/.f64 d (pow.f64 (cbrt.f64 D) 2)))) (/.f64 (.f64 (pow.f64 M 2) h) d))
	25.5b	(.f64 (.f64 1/4 (/.f64 (pow.f64 D 2) d)) (/.f64 (.f64 M (.f64 h M)) d))

Compiler

Compiled 5811 to 3406 computations (41.4% saved)

regimes2.6s (12.1%)

Accuracy

Total 8.1b remaining (28.5%)

Threshold costs 0b (0%)

Counts

158 → 3

Compiler

Compiled 52663 to 36212 computations (31.2% saved)

bsearch421.0ms (2%)

Steps

Iters	Range		Point
8	1.036823540220767e+137	5.605491028977528e+141	7.0868357241638995e+140
10	-4.715589841286331e+158	-6.1338348849536105e+147	-1.360662088649393e+154

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	79
1	52	79
2	50	79

end334.0ms (1.6%)

Compiler: Compiled 852 to 540 computations (36.6% saved)

Details

analyze2.6s (12.3%)

sample9.6s (45.2%)

simplify41.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series807.0ms (3.8%)

rewrite102.0ms (0.5%)

simplify255.0ms (1.2%)

prune495.0ms (2.3%)

localize15.0ms (0.1%)

series598.0ms (2.8%)

rewrite199.0ms (0.9%)

simplify369.0ms (1.7%)

prune659.0ms (3.1%)

localize10.0ms (0%)

series312.0ms (1.5%)

rewrite53.0ms (0.3%)

simplify144.0ms (0.7%)

prune495.0ms (2.3%)

localize9.0ms (0%)

series187.0ms (0.9%)

rewrite31.0ms (0.1%)

simplify240.0ms (1.1%)

prune634.0ms (3%)

regimes2.6s (12.1%)

bsearch421.0ms (2%)

simplify3.0ms (0%)

end334.0ms (1.6%)

Profiling