Details

analyze2.7s (14.3%)

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)

sample8.8s (47.3%)

Results

3.0s	16306×	body	128	invalid
2.0s	2170×	body	4096	valid
1.4s	1246×	body	8192	valid
987.0ms	1304×	body	2048	valid
516.0ms	2505×	body	128	valid
377.0ms	598×	body	1024	valid
134.0ms	286×	body	512	valid
46.0ms	147×	body	256	valid
40.0ms	54×	body	2048	invalid
37.0ms	64×	body	1024	invalid
28.0ms	37×	body	512	invalid
19.0ms	22×	body	4096	invalid
9.0ms	9×	body	8192	exit
9.0ms	28×	body	256	invalid

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

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

59.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.7b	(.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)))))
▶	59.8b	(.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)))))

Status

Error

Program

61.7b

(*.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)))))

▶

59.8b

(*.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)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.5b	(.f64 (.f64 w h) (*.f64 D D))
✓	14.2b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	14.3b	(.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)))))
✓	31.2b	(+.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))))

series954.0ms (5.1%)

Counts

4 → 240

Calls

4 calls:

482.0ms	(.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)))))
274.0ms	(+.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))))
177.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
20.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite118.0ms (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:

40.0ms	(.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))))
11.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
5.0ms	(.f64 (.f64 w h) (*.f64 D D))

simplify329.0ms (1.8%)

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

prune675.0ms (3.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	451	12	463
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	452	13	465

Error

29.5b

Counts

465 → 13

Alt Table

Status	Error	Program
	59.7b	(.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)))))
▶	35.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	60.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 w (.f64 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)))))
	62.6b	(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))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (/.f64 (.f64 c0 (.f64 d d)) (.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)))))
	49.4b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	60.1b	(/.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))
	41.9b	(.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))))
	60.6b	(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))))
	61.7b	(.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)))))
	59.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	63.3b	(/.f64 (.f64 c0 (+.f64 (.f64 (.f64 c0 (.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 (.f64 (.f64 w h) (.f64 D D)) (sqrt.f64 (-.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 (/.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 (.f64 M M) (.f64 M M))))))) (.f64 (.f64 2 w) (.f64 (.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))))))
	61.5b	(.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (.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 31944 to 7057 computations (77.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	9.4b	(*.f64 (pow.f64 M 2) h)
✓	12.7b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
✓	14.0b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

series154.0ms (0.8%)

Counts

3 → 40

Calls

3 calls:

115.0ms	(/.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)

rewrite28.0ms (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:

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))
5.0ms	(*.f64 (pow.f64 M 2) h)

simplify115.0ms (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

prune341.0ms (1.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	142	18	160
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	148	25	173

Error

20.4b

Counts

173 → 25

Alt Table

Status	Error	Program
	33.0b	(.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)))
	58.7b	(.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))))
	61.7b	(.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)))))
	47.6b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h)))) (pow.f64 d 2)))
	51.0b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	56.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (exp.f64 (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	53.0b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	58.1b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	59.7b	(.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)))))
	33.2b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	60.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 w (.f64 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)))))
	62.6b	(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))
	33.8b	(.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)))
	57.4b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	33.1b	(.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))))
	34.1b	(.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)))
	60.1b	(/.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))
	32.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	49.1b	(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) (pow.f64 d 2)))
	61.5b	(.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (.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)))))))
	55.8b	(.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)))))
▶	32.4b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	35.0b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	33.3b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	59.3b	(.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 5040 to 3100 computations (38.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.4b	(/.f64 (.f64 h (.f64 M M)) d)
✓	7.8b	(/.f64 (*.f64 D D) d)
✓	9.4b	(.f64 h (.f64 M M))
✓	10.8b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series159.0ms (0.9%)

Counts

4 → 132

Calls

4 calls:

115.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
25.0ms	(/.f64 (.f64 h (.f64 M M)) d)
10.0ms	(/.f64 (*.f64 D D) d)
9.0ms	(.f64 h (.f64 M M))

rewrite34.0ms (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:

9.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
8.0ms	(/.f64 (.f64 h (.f64 M M)) d)
4.0ms	(.f64 h (.f64 M M))
3.0ms	(/.f64 (*.f64 D D) d)

simplify132.0ms (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

prune265.0ms (1.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	154	6	160
Fresh	7	17	24
Picked	1	0	1
Done	0	0	0
Total	162	23	185

Error

17.5b

Counts

185 → 23

Alt Table

Status	Error	Program
	33.0b	(.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)))
	61.7b	(.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)))))
	51.0b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	29.7b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	32.0b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	53.0b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	58.1b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	59.7b	(.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)))))
	30.2b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d D)) (/.f64 (.f64 h (.f64 M M)) d)))
	60.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 w (.f64 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)))))
	62.6b	(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))
	33.3b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	58.6b	(.f64 1/4 (exp.f64 (+.f64 (log.f64 (/.f64 (.f64 D D) d)) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
	33.1b	(.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))))
	60.1b	(/.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))
▶	29.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	32.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	49.1b	(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) (pow.f64 d 2)))
	61.5b	(.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (.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)))))))
	57.4b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	48.5b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	35.0b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	59.3b	(.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 5113 to 1733 computations (66.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 h M) M)
✓	5.4b	(/.f64 (.f64 (.f64 h M) M) d)
	7.8b	(/.f64 (*.f64 D D) d)
✓	10.8b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 h M) M) d))

series340.0ms (1.8%)

Counts

3 → 108

Calls

3 calls:

308.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 h M) M) d))
25.0ms	(/.f64 (.f64 (.f64 h M) M) d)
8.0ms	(.f64 (.f64 h M) M)

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-cbrt-cube_binary64`
71×	`add-exp-log_binary64`
31×	`cbrt-unprod_binary64`
31×	`prod-exp_binary64`
20×	`cbrt-undiv_binary64`

Counts

3 → 99

Calls

3 calls:

11.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 h M) M) d))
6.0ms	(/.f64 (.f64 (.f64 h M) M) d)
4.0ms	(.f64 (.f64 h M) M)

simplify192.0ms (1%)

Algorithm

1×	egg-herbie

Rules

717×	`associate-/r*_binary64`
634×	`associate-/r/_binary64`
510×	`*-commutative_binary64`
264×	`log-prod_binary64`
237×	`associate-l_binary64`

Counts

207 → 154

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	158	3704
1	412	3065
2	1771	3065
3	4477	3065
4	4939	3065
5	5000	3065
6	4982	3065

prune331.0ms (1.8%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	174	9	183
Fresh	4	18	22
Picked	1	0	1
Done	0	0	0
Total	179	27	206

Error

15.6b

Counts

206 → 27

Alt Table

Status	Error	Program
	46.1b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 (*.f64 h M) (sqrt.f64 d))) (/.f64 M (sqrt.f64 d))))
	61.7b	(.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)))))
	32.0b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	53.0b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	27.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 (*.f64 M h) (/.f64 M d))))
	58.1b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	59.7b	(.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)))))
	60.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 w (.f64 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)))))
	62.6b	(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))
	25.9b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 (*.f64 h M) M) d))))
	26.7b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d D)) (/.f64 (.f64 (.f64 h M) M) d)))
	26.4b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (*.f64 M h)) (/.f64 M d)))
	57.4b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	27.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h M) (/.f64 d M))))
	33.3b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	26.4b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h M) (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 M (cbrt.f64 d))))
	58.6b	(.f64 1/4 (exp.f64 (+.f64 (log.f64 (/.f64 (.f64 D D) d)) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
	33.1b	(.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))))
	60.1b	(/.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))
	49.1b	(*.f64 1/4 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) (pow.f64 d 2)))
	61.5b	(.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (.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)))))))
	26.7b	(.f64 1/4 (.f64 (.f64 D (/.f64 D d)) (/.f64 (.f64 (*.f64 h M) M) d)))
	35.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (log.f64 (exp.f64 (/.f64 (.f64 (*.f64 h M) M) d)))))
	51.0b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	48.5b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	35.0b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	59.3b	(.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 4898 to 1457 computations (70.3% saved)

regimes2.5s (13.2%)

Accuracy

Total 6.8b remaining (28.8%)

Threshold costs 0b (0%)

Counts

139 → 4

Compiler

Compiled 59760 to 31002 computations (48.1% saved)

bsearch11.0ms (0.1%)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	367
1	78	367
2	84	367
3	88	367
4	90	367
5	90	367

end385.0ms (2.1%)

Compiler: Compiled 1370 to 664 computations (51.5% saved)

Details

analyze2.7s (14.3%)

sample8.8s (47.3%)

simplify41.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0.1%)

series954.0ms (5.1%)

rewrite118.0ms (0.6%)

simplify329.0ms (1.8%)

prune675.0ms (3.6%)

localize9.0ms (0.1%)

series154.0ms (0.8%)

rewrite28.0ms (0.1%)

simplify115.0ms (0.6%)

prune341.0ms (1.8%)

localize10.0ms (0.1%)

series159.0ms (0.9%)

rewrite34.0ms (0.2%)

simplify132.0ms (0.7%)

prune265.0ms (1.4%)

localize10.0ms (0.1%)

series340.0ms (1.8%)

rewrite31.0ms (0.2%)

simplify192.0ms (1%)

prune331.0ms (1.8%)

regimes2.5s (13.2%)

bsearch11.0ms (0.1%)

simplify9.0ms (0.1%)

end385.0ms (2.1%)

Profiling