Details

analyze2.4s (14.7%)

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)

sample257.0ms (1.6%)

Algorithm

1×

intervals

Results

41.0ms	62×	body	4096	valid
33.0ms	46×	body	8192	valid
31.0ms	320×	body	128	nan
23.0ms	38×	body	2048	valid
11.0ms	115×	body	128	invalid
8.0ms	87×	body	128	valid
5.0ms	6×	body	1024	valid
3.0ms	9×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	3×	body	2048	invalid
1.0ms	2×	body	512	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify42.0ms (0.3%)

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

59.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	63.1b	(.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)))))
▶	59.9b	(.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

63.1b

(*.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)))))

▶

59.9b

(*.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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.2b	(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)))
✓	15.1b	(.f64 (.f64 w h) (*.f64 D D))
✓	18.3b	(/.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))))

series780.0ms (4.7%)

Counts

4 → 240

Calls

4 calls:

294.0ms	(+.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))))
276.0ms	(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)))
187.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
22.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite93.0ms (0.6%)

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:

38.0ms	(+.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))))
25.0ms	(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))

simplify271.0ms (1.6%)

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

prune740.0ms (4.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	406	11	417
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	407	12	419

Error

36.0b

Counts

419 → 12

Alt Table

Status	Error	Program
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (log.f64 (.f64 c0 (.f64 d d))) (+.f64 (+.f64 (log.f64 w) (log.f64 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)))))
	63.1b	(.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)))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 c0 (/.f64 (.f64 w h) (/.f64 (.f64 d d) (.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)))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	62.8b	(.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)))))
	51.9b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	62.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1 (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))))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (sqrt.f64 (+.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 (.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)))))))
	63.0b	(.f64 (/.f64 c0 (.f64 2 w)) (exp.f64 (log.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)))))))
	60.9b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.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)))))
	60.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (neg.f64 (/.f64 (.f64 (.f64 d d) c0) (.f64 (.f64 D D) (.f64 w h))))))
▶	42.2b	(.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))))

Compiler

Compiled 28025 to 6581 computations (76.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(.f64 w (.f64 h (pow.f64 M 2)))
✓	12.2b	(.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))))
✓	14.1b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
✓	15.4b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))

series611.0ms (3.7%)

Counts

4 → 160

Calls

4 calls:

289.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
243.0ms	(.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))))
58.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
21.0ms	(.f64 w (.f64 h (pow.f64 M 2)))

rewrite200.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

1742×	`add-exp-log_binary64`
1270×	`prod-exp_binary64`
388×	`div-exp_binary64`
239×	`add-cbrt-cube_binary64`
201×	`pow-exp_binary64`

Counts

4 → 396

Calls

4 calls:

19.0ms	(.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))))
14.0ms	(/.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 w (.f64 h (pow.f64 M 2)))

simplify387.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-/l/_binary64`
565×	`times-frac_binary64`
504×	`associate-r_binary64`
408×	`associate-l_binary64`
321×	`log-div_binary64`

Counts

556 → 302

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	382	19077
1	725	15505
2	3117	15505
3	4814	15505
4	5204	15505

prune587.0ms (3.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	294	8	302
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	296	18	314

Error

27.1b

Counts

314 → 18

Alt Table

Status	Error	Program
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (log.f64 (.f64 c0 (.f64 d d))) (+.f64 (+.f64 (log.f64 w) (log.f64 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)))))
	63.1b	(.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)))))
	44.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 w h) (pow.f64 M 2))) (*.f64 (pow.f64 d 2) c0))))
	57.3b	(.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) (log.f64 (pow.f64 M 2)))))) (.f64 (pow.f64 d 2) c0))))
	60.4b	(.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))))
	62.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1 (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))))))
▶	33.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	60.9b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.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 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 c0 (/.f64 (.f64 w h) (/.f64 (.f64 d d) (.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)))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	62.8b	(.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)))))
	51.9b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (sqrt.f64 (+.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 (.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)))))))
	63.0b	(.f64 (/.f64 c0 (.f64 2 w)) (exp.f64 (log.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)))))))
	37.6b	(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)))
	41.7b	(.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))))
	60.1b	(.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))))))
	40.3b	(.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))))

Compiler

Compiled 12796 to 7709 computations (39.8% saved)

localize9.0ms (0.1%)

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)))
✓	5.9b	(*.f64 (pow.f64 M 2) h)
✓	13.0b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	13.3b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series308.0ms (1.9%)

Counts

4 → 72

Calls

4 calls:

143.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
124.0ms	(/.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))
8.0ms	(*.f64 (pow.f64 M 2) h)

rewrite56.0ms (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:

13.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
13.0ms	(.f64 1/4 (/.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))
4.0ms	(*.f64 (pow.f64 M 2) h)

simplify148.0ms (0.9%)

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

prune456.0ms (2.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	217	14	231
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	224	25	249

Error

20.3b

Counts

249 → 25

Alt Table

Status	Error	Program
	30.5b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	62.8b	(.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)))))
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (log.f64 (.f64 c0 (.f64 d d))) (+.f64 (+.f64 (log.f64 w) (log.f64 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)))))
	63.1b	(.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 c0 (.f64 2 w)) (.f64 1 (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))))))
	33.1b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	60.5b	(.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))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (sqrt.f64 (+.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 (.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)))))))
	33.9b	(.f64 1/4 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 D 2)) (cbrt.f64 (pow.f64 D 2))) (.f64 (cbrt.f64 (pow.f64 D 2)) (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	32.1b	(.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)))
▶	30.4b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	30.5b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	58.0b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	40.3b	(.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))))
	33.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	51.4b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 c0 (/.f64 (.f64 w h) (/.f64 (.f64 d d) (.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)))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	47.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h)))) (pow.f64 d 2)))
	44.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 w h) (pow.f64 M 2))) (*.f64 (pow.f64 d 2) c0))))
	63.0b	(.f64 (/.f64 c0 (.f64 2 w)) (exp.f64 (log.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)))))))
	60.9b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.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)))))
	55.2b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	54.3b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	58.0b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))

Compiler

Compiled 6806 to 4150 computations (39% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
✓	5.4b	(.f64 D (.f64 (pow.f64 M 2) h))
	5.9b	(*.f64 (pow.f64 M 2) h)
✓	13.3b	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))

series176.0ms (1.1%)

Counts

3 → 100

Calls

3 calls:

121.0ms	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))
31.0ms	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
23.0ms	(.f64 D (.f64 (pow.f64 M 2) h))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
31×	`add-cbrt-cube_binary64`
18×	`div-exp_binary64`
15×	`cbrt-unprod_binary64`

Counts

3 → 96

Calls

3 calls:

8.0ms	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))
6.0ms	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
4.0ms	(.f64 D (.f64 (pow.f64 M 2) h))

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

649×	`associate-*l/_binary64`
480×	`associate-*r/_binary64`
443×	`*-commutative_binary64`
406×	`associate-/l/_binary64`
385×	`associate-/r/_binary64`

Counts

196 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	3573
1	317	3183
2	1481	3183
3	4665	3158
4	5070	3158

prune357.0ms (2.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	7	17	24
Picked	1	0	1
Done	0	0	0
Total	180	26	206

Error

17.6b

Counts

206 → 26

Alt Table

Status	Error	Program
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (log.f64 (.f64 c0 (.f64 d d))) (+.f64 (+.f64 (log.f64 w) (log.f64 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)))))
	63.1b	(.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)))))
	27.5b	(.f64 1/4 (.f64 (/.f64 D (.f64 d (cbrt.f64 d))) (/.f64 (.f64 D (.f64 h (.f64 M M))) (pow.f64 (cbrt.f64 d) 2))))
	62.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1 (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))))))
	25.8b	(.f64 1/4 (/.f64 (.f64 (.f64 D (.f64 h (*.f64 M M))) (/.f64 D d)) d))
	33.9b	(.f64 1/4 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 D 2)) (cbrt.f64 (pow.f64 D 2))) (.f64 (cbrt.f64 (pow.f64 D 2)) (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	27.6b	(.f64 1/4 (.f64 (/.f64 D (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) 2)) (/.f64 (.f64 D (*.f64 (pow.f64 M 2) h)) (pow.f64 (cbrt.f64 d) 2))))
	60.5b	(.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))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (sqrt.f64 (+.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 (.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)))))))
	29.5b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 M (*.f64 h M)))) (pow.f64 d 2)))
	63.0b	(.f64 (/.f64 c0 (.f64 2 w)) (exp.f64 (log.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)))))))
	29.2b	(.f64 1/4 (/.f64 (.f64 D (.f64 (.f64 D (pow.f64 M 2)) h)) (pow.f64 d 2)))
	46.4b	(.f64 1/4 (.f64 (/.f64 D (pow.f64 (sqrt.f64 d) 2)) (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))
	51.4b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 c0 (/.f64 (.f64 w h) (/.f64 (.f64 d d) (.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)))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	25.6b	(.f64 1/4 (.f64 (/.f64 D d) (/.f64 (.f64 D (.f64 (pow.f64 M 2) h)) d)))
	62.8b	(.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)))))
	47.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h)))) (pow.f64 d 2)))
	44.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 w h) (pow.f64 M 2))) (*.f64 (pow.f64 d 2) c0))))
	60.9b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.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)))))
	25.6b	(.f64 1/4 (/.f64 D (/.f64 d (.f64 (.f64 h (.f64 M M)) (/.f64 D d)))))
	55.2b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	58.0b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	54.3b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (*.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	36.6b	(.f64 1/4 (/.f64 (.f64 D (exp.f64 (log.f64 (.f64 D (.f64 h (*.f64 M M)))))) (pow.f64 d 2)))

Compiler

Compiled 4727 to 2676 computations (43.4% saved)

regimes1.5s (8.8%)

Accuracy

Total 8.4b remaining (31.1%)

Threshold costs 0b (0%)

Counts

125 → 1

Compiler

Compiled 39177 to 26606 computations (32.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	16	22
2	16	22

end1.0ms (0%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

sample7.0s (42.3%)

Algorithm

1×

intervals

Results

1.4s	2099×	body	4096	valid
1.3s	11613×	body	128	nan
890.0ms	1151×	body	8192	valid
673.0ms	1312×	body	2048	valid
524.0ms	3926×	body	128	invalid
280.0ms	617×	body	1024	valid
243.0ms	2379×	body	128	valid
82.0ms	285×	body	512	valid
33.0ms	157×	body	256	valid
32.0ms	47×	body	2048	invalid
25.0ms	61×	body	1024	invalid
11.0ms	25×	body	256	invalid
9.0ms	31×	body	512	invalid
6.0ms	11×	body	4096	invalid
4.0ms	6×	body	8192	exit

Compiler

Compiled 1003 to 577 computations (42.5% saved)

Details

analyze2.4s (14.7%)

sample257.0ms (1.6%)

simplify42.0ms (0.3%)

prune5.0ms (0%)

localize19.0ms (0.1%)

series780.0ms (4.7%)

rewrite93.0ms (0.6%)

simplify271.0ms (1.6%)

prune740.0ms (4.5%)

localize15.0ms (0.1%)

series611.0ms (3.7%)

rewrite200.0ms (1.2%)

simplify387.0ms (2.3%)

prune587.0ms (3.5%)

localize9.0ms (0.1%)

series308.0ms (1.9%)

rewrite56.0ms (0.3%)

simplify148.0ms (0.9%)

prune456.0ms (2.8%)

localize9.0ms (0.1%)

series176.0ms (1.1%)

rewrite26.0ms (0.2%)

simplify109.0ms (0.7%)

prune357.0ms (2.2%)

regimes1.5s (8.8%)

simplify2.0ms (0%)

end1.0ms (0%)

sample7.0s (42.3%)

Profiling