Details

analyze2.8s (13.1%)

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)

sample9.3s (43.8%)

Results

3.2s	16324×	body	128	invalid
2.1s	2179×	body	4096	valid
1.4s	1178×	body	8192	valid
1.1s	1385×	body	2048	valid
495.0ms	2397×	body	128	valid
421.0ms	630×	body	1024	valid
176.0ms	335×	body	512	valid
57.0ms	152×	body	256	valid
43.0ms	60×	body	1024	invalid
42.0ms	46×	body	2048	invalid
21.0ms	45×	body	512	invalid
18.0ms	18×	body	4096	invalid
7.0ms	22×	body	256	invalid
7.0ms	6×	body	8192	exit

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify45.0ms (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

59.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	59.7b	(.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)))))
	61.8b	(.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

▶

59.7b

(*.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)))))

61.8b

(*.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)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.8b	(.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)))))
✓	14.1b	(.f64 (.f64 w h) (*.f64 D D))
✓	15.6b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	29.5b	(+.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))))

series995.0ms (4.7%)

Counts

4 → 240

Calls

4 calls:

484.0ms	(.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)))))
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))))
190.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
19.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite120.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`add-cbrt-cube_binary64`
94×	`add-exp-log_binary64`
51×	`cbrt-unprod_binary64`
51×	`prod-exp_binary64`
18×	`pow1_binary64`

Counts

4 → 130

Calls

4 calls:

44.0ms	(.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)))))
37.0ms	(+.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))))
13.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
5.0ms	(.f64 (.f64 w h) (*.f64 D D))

simplify342.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

488×	`associate-/r*_binary64`
478×	`associate-/l*_binary64`
460×	`fma-def_binary64`
295×	`associate-*l/_binary64`
278×	`associate-*r/_binary64`

Counts

370 → 279

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	477	18780
1	1465	16679
2	4886	16625
3	5160	16625

prune568.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	452	11	463
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	453	12	465

Error

27.8b

Counts

465 → 12

Alt Table

Status	Error	Program
	59.6b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
▶	33.6b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	59.6b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
	61.8b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 h (.f64 w w))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	40.1b	(.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))))
	61.8b	(.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)))))
	62.9b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M)))) (cbrt.f64 (/.f64 c0 (*.f64 2 w)))))
	61.6b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	49.1b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	60.2b	(.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)))))
	60.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.5b	(.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 (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)))))) (*.f64 M M)))))

Compiler

Compiled 31510 to 7011 computations (77.7% 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)))
✓	7.9b	(*.f64 (pow.f64 M 2) h)
✓	14.9b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	15.5b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series308.0ms (1.5%)

Counts

4 → 72

Calls

4 calls:

150.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
119.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
30.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite52.0ms (0.2%)

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:

11.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
7.0ms	(/.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)

simplify138.0ms (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

prune748.0ms (3.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	211	20	231
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	215	28	243

Error

19.5b

Counts

243 → 28

Alt Table

Status	Error	Program
	31.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) (.f64 d (cbrt.f64 d))) (/.f64 (.f64 h (.f64 M M)) (pow.f64 (cbrt.f64 d) 2))))
	46.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h)))) (pow.f64 d 2)))
	62.9b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M)))) (cbrt.f64 (/.f64 c0 (*.f64 2 w)))))
	30.6b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	59.6b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	52.0b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 (pow.f64 M 2) h))) (log.f64 (pow.f64 d 2)))))
	61.8b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 h (.f64 w w))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	57.6b	(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))))
	61.6b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	58.5b	(.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))))
	58.2b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	32.9b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	49.0b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 (sqrt.f64 d) 2)) (pow.f64 (sqrt.f64 d) 2)))
	52.0b	(.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)))))
	31.3b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	31.0b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	57.3b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	33.2b	(.f64 1/4 (.f64 (.f64 D D) (/.f64 (.f64 h (.f64 M M)) (.f64 d d))))
	61.8b	(.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)))))
	31.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	60.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	31.7b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) 2) (.f64 (pow.f64 (cbrt.f64 D) 2) (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	60.5b	(.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 (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)))))) (*.f64 M M)))))
▶	30.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	57.3b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	55.6b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	31.7b	(.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))))
	60.2b	(.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)))))

Compiler

Compiled 6798 to 4222 computations (37.9% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.6b	(/.f64 (.f64 h (.f64 M M)) d)
✓	7.9b	(.f64 h (.f64 M M))
✓	9.2b	(/.f64 (*.f64 D D) d)
✓	11.6b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series219.0ms (1%)

Counts

4 → 132

Calls

4 calls:

133.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
62.0ms	(/.f64 (.f64 h (.f64 M M)) d)
12.0ms	(.f64 h (.f64 M M))
11.0ms	(/.f64 (*.f64 D D) d)

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:

10.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
5.0ms	(.f64 h (.f64 M M))
5.0ms	(/.f64 (.f64 h (.f64 M M)) d)
3.0ms	(/.f64 (*.f64 D D) d)

simplify133.0ms (0.6%)

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

prune342.0ms (1.6%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	149	11	160
Fresh	6	21	27
Picked	1	0	1
Done	0	0	0
Total	156	32	188

Error

17.1b

Counts

188 → 32

Alt Table

Status	Error	Program
	28.9b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 h (/.f64 (*.f64 M M) d))))
	31.7b	(.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))))
	62.9b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M)))) (cbrt.f64 (/.f64 c0 (*.f64 2 w)))))
	30.6b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	30.6b	(.f64 1/4 (.f64 (.f64 (.f64 D D) (/.f64 (.f64 h (.f64 M M)) d)) (/.f64 1 d)))
	26.2b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	28.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	59.6b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	45.8b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
▶	25.8b	(.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))))
	61.8b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 h (.f64 w w))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	57.6b	(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))))
	58.5b	(.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))))
	27.0b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d D)) (/.f64 (.f64 h (.f64 M M)) d)))
	61.6b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	58.2b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	32.9b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	52.0b	(.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)))))
	60.2b	(.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)))))
	32.5b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (expm1.f64 (log1p.f64 (.f64 h (*.f64 M M)))) d)))
	28.0b	(.f64 1/4 (.f64 (/.f64 (.f64 D (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d)))
	61.8b	(.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)))))
	31.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	60.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	31.7b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) 2) (.f64 (pow.f64 (cbrt.f64 D) 2) (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	60.5b	(.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 (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)))))) (*.f64 M M)))))
	57.3b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	55.6b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	46.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h)))) (pow.f64 d 2)))
	56.2b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (/.f64 (.f64 h (.f64 M M)) d)))
	48.6b	(.f64 1/4 (.f64 (.f64 (/.f64 D (sqrt.f64 d)) (sqrt.f64 (/.f64 (.f64 h (.f64 M M)) d))) (.f64 (/.f64 D (sqrt.f64 d)) (sqrt.f64 (/.f64 (.f64 h (.f64 M M)) d)))))
	57.3b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))

Compiler

Compiled 5549 to 2065 computations (62.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.0b	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	5.6b	(/.f64 (.f64 h (.f64 M M)) d)
	7.9b	(.f64 h (.f64 M M))
✓	7.9b	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))

series1.5s (7.2%)

Counts

2 → 96

Calls

2 calls:

1.3s	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))
173.0ms	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))

rewrite61.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

187×	`add-exp-log_binary64`
153×	`add-cbrt-cube_binary64`
92×	`cbrt-unprod_binary64`
92×	`prod-exp_binary64`
58×	`cbrt-undiv_binary64`

Counts

2 → 143

Calls

2 calls:

18.0ms	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
13.0ms	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))

simplify163.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/r/_binary64`
350×	`associate-r_binary64`
307×	`associate-*l/_binary64`
307×	`times-frac_binary64`
295×	`associate-*r/_binary64`

Counts

239 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	7889
1	588	4982
2	2626	4964
3	4878	4964
4	4965	4964

prune598.0ms (2.8%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	256	10	266
Fresh	9	22	31
Picked	1	0	1
Done	0	0	0
Total	266	32	298

Error

15.8b

Counts

298 → 32

Alt Table

Status	Error	Program
	28.9b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 h (/.f64 (*.f64 M M) d))))
	31.7b	(.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))))
	30.5b	(.f64 1/4 (/.f64 (.f64 (.f64 (.f64 M M) h) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 D (cbrt.f64 d)))) (.f64 (cbrt.f64 d) d)))
	56.2b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (/.f64 (.f64 h (.f64 M M)) d)))
	62.9b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M)))) (cbrt.f64 (/.f64 c0 (*.f64 2 w)))))
	27.3b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (/.f64 (.f64 (*.f64 M M) h) d))) d))
	30.6b	(.f64 1/4 (.f64 (.f64 (.f64 D D) (/.f64 (.f64 h (.f64 M M)) d)) (/.f64 1 d)))
	26.2b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	30.9b	(.f64 1/4 (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (.f64 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d)) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d))))))
	26.2b	(.f64 1/4 (.f64 D (/.f64 (.f64 D (/.f64 (.f64 (*.f64 M M) h) d)) d)))
	28.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	59.6b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	45.8b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	36.1b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (exp.f64 (log.f64 (.f64 h (.f64 M M)))) d))))
	61.6b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	58.5b	(.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))))
	32.9b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	52.0b	(.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)))))
	44.1b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h (sqrt.f64 d))) (/.f64 (.f64 M M) (sqrt.f64 d)))))
	61.8b	(.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)))))
	31.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	60.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	22.1b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (/.f64 D d) h) (/.f64 (.f64 M M) (cbrt.f64 d)))))
	24.0b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 (.f64 h M) M) d))))
	60.5b	(.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 (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)))))) (*.f64 M M)))))
	23.4b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (*.f64 M M) (cbrt.f64 d)))))
	57.3b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	55.6b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	46.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h)))) (pow.f64 d 2)))
	61.8b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 h (.f64 w w))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	23.9b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 h (/.f64 D (cbrt.f64 d))) (/.f64 (.f64 M M) d))))
	60.2b	(.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)))))

Compiler

Compiled 9466 to 2135 computations (77.4% saved)

regimes2.2s (10.5%)

Accuracy

Total 5.6b remaining (24.2%)

Threshold costs 0b (0%)

Counts

149 → 2

Compiler

Compiled 59438 to 33739 computations (43.2% saved)

bsearch7.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	77
1	36	77
2	36	77

end429.0ms (2%)

Compiler: Compiled 1174 to 666 computations (43.3% saved)

Details

analyze2.8s (13.1%)

sample9.3s (43.8%)

simplify45.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series995.0ms (4.7%)

rewrite120.0ms (0.6%)

simplify342.0ms (1.6%)

prune568.0ms (2.7%)

localize10.0ms (0%)

series308.0ms (1.5%)

rewrite52.0ms (0.2%)

simplify138.0ms (0.7%)

prune748.0ms (3.5%)

localize10.0ms (0%)

series219.0ms (1%)

rewrite36.0ms (0.2%)

simplify133.0ms (0.6%)

prune342.0ms (1.6%)

localize23.0ms (0.1%)

series1.5s (7.2%)

rewrite61.0ms (0.3%)

simplify163.0ms (0.8%)

prune598.0ms (2.8%)

regimes2.2s (10.5%)

bsearch7.0ms (0%)

simplify3.0ms (0%)

end429.0ms (2%)

Profiling