Details

analyze2.8s (13%)

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 (44%)

Results

3.3s	16252×	body	128	invalid
2.2s	2164×	body	4096	valid
1.5s	1238×	body	8192	valid
1.1s	1280×	body	2048	valid
528.0ms	2455×	body	128	valid
455.0ms	676×	body	1024	valid
139.0ms	285×	body	512	valid
59.0ms	158×	body	256	valid
49.0ms	62×	body	2048	invalid
36.0ms	58×	body	1024	invalid
22.0ms	46×	body	512	invalid
11.0ms	12×	body	4096	invalid
8.0ms	7×	body	8192	exit
5.0ms	14×	body	256	invalid

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify42.0ms (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

59.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	60.1b	(.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)))))
	61.4b	(.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

▶

60.1b

(*.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)))))

61.4b

(*.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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.6b	(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)))
✓	13.2b	(.f64 (.f64 w h) (*.f64 D D))
✓	15.1b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	33.4b	(+.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))))

series1.1s (5%)

Counts

4 → 240

Calls

4 calls:

568.0ms	(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)))
304.0ms	(+.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))))
195.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
28.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite104.0ms (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:

42.0ms	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))
26.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))
13.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
6.0ms	(.f64 (.f64 w h) (*.f64 D D))

simplify314.0ms (1.4%)

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

prune638.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	409	8	417
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	410	9	419

Error

37.4b

Counts

419 → 9

Alt Table

Status	Error	Program
	61.4b	(.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 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	62.4b	(.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)))))
	61.5b	(.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))))))
▶	43.5b	(.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))))
	52.5b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (cbrt.f64 (pow.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)))) 3)))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (.f64 d d) c0)) -1/2))))
	60.1b	(.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 27581 to 6431 computations (76.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.0b	(*.f64 (pow.f64 d 2) c0)
✓	10.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
✓	13.8b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
✓	17.4b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))

series632.0ms (2.9%)

Counts

4 → 144

Calls

4 calls:

291.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
270.0ms	(.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 (pow.f64 d 2) c0)

rewrite207.0ms (1%)

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:

22.0ms	(.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))))
12.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
7.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
4.0ms	(*.f64 (pow.f64 d 2) c0)

simplify322.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

548 → 317

Iterations

Useful iterations: 1 (0.0ms)

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

prune720.0ms (3.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	301	16	317
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	302	24	326

Error

29.0b

Counts

326 → 24

Alt Table

Status	Error	Program
	61.1b	(.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))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	52.5b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	38.6b	(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)))
	42.2b	(.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))))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (cbrt.f64 (pow.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)))) 3)))
	43.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (log.f64 (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (.f64 d d) c0))))))
	63.6b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2)))) (log.f64 (.f64 (pow.f64 d 2) c0))))))
	57.7b	(.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))))
▶	36.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	61.7b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (log.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (*.f64 (log.f64 d) 2) (log.f64 c0))))))
	60.9b	(.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))))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (.f64 d d) c0)) -1/2))))
	43.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 d (.f64 d c0)))))
	61.4b	(.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 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	54.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 (sqrt.f64 d) 2) (.f64 d c0)))))
	42.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (.f64 w (.f64 (.f64 M M) h)) (/.f64 (.f64 D D) (*.f64 d d))) c0)))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 (.f64 w h) D) D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	62.4b	(.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)))))
	61.5b	(.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))))))
	61.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (+.f64 (log.f64 2) (log.f64 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 w) (log.f64 (.f64 h (pow.f64 M 2))))) (+.f64 (.f64 (log.f64 d) 2) (log.f64 c0))))))
	61.5b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (log.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (*.f64 (log.f64 d) 2) (log.f64 c0))))))
	63.6b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2)))) (+.f64 (.f64 (log.f64 d) 2) (log.f64 c0))))))
	43.3b	(.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))))

Compiler

Compiled 13478 to 8357 computations (38% 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)))
✓	7.8b	(*.f64 (pow.f64 M 2) h)
✓	15.9b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	16.2b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series325.0ms (1.5%)

Counts

4 → 72

Calls

4 calls:

149.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
131.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
36.0ms	(.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:

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

simplify155.0ms (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

prune524.0ms (2.4%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	214	17	231
Fresh	11	12	23
Picked	1	0	1
Done	0	0	0
Total	226	29	255

Error

22.6b

Counts

255 → 29

Alt Table

Status	Error	Program
	61.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (+.f64 (log.f64 2) (log.f64 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 w) (log.f64 (.f64 h (pow.f64 M 2))))) (+.f64 (.f64 (log.f64 d) 2) (log.f64 c0))))))
	34.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	61.1b	(.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))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	48.9b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) (pow.f64 (sqrt.f64 d) 2)))
	48.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h)))) (pow.f64 d 2)))
	33.9b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	58.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	61.5b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (log.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (*.f64 (log.f64 d) 2) (log.f64 c0))))))
	56.0b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (cbrt.f64 (pow.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)))) 3)))
	43.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (log.f64 (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (.f64 d d) c0))))))
	63.6b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2)))) (log.f64 (.f64 (pow.f64 d 2) c0))))))
	61.4b	(.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)))))
	35.2b	(.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)))
	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)))))
	38.0b	(log.f64 (exp.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))))
	60.1b	(.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)))))
	56.0b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	51.6b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	62.4b	(.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)))))
	61.5b	(.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))))))
▶	32.7b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	49.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (sqrt.f64 M) 2) (.f64 (pow.f64 (sqrt.f64 M) 2) h))) (pow.f64 d 2)))
	35.8b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	34.0b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	34.0b	(.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))))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (.f64 d d) c0)) -1/2))))
	55.1b	(.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)))
	58.9b	(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))))

Compiler

Compiled 6828 to 4336 computations (36.5% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.0b	(/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d)) d)
✓	7.8b	(/.f64 (*.f64 D D) d)
✓	7.8b	(.f64 h (.f64 M M))
✓	14.2b	(.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d))

series210.0ms (1%)

Counts

4 → 144

Calls

4 calls:

125.0ms	(/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d)) d)
64.0ms	(.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d))
12.0ms	(/.f64 (*.f64 D D) d)
9.0ms	(.f64 h (.f64 M M))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-cbrt-cube_binary64`
97×	`add-exp-log_binary64`
46×	`cbrt-unprod_binary64`
46×	`prod-exp_binary64`
24×	`cbrt-undiv_binary64`

Counts

4 → 124

Calls

4 calls:

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

simplify153.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

542×	`*-commutative_binary64`
351×	`fma-def_binary64`
241×	`fma-neg_binary64`
224×	`unswap-sqr_binary64`
219×	`associate-l_binary64`

Counts

268 → 176

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	169	4803
1	380	3954
2	1769	3954
3	3122	3917
4	4684	3896
5	4971	3896

prune590.0ms (2.7%)

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	159	17	176
Fresh	11	17	28
Picked	1	0	1
Done	0	0	0
Total	171	34	205

Error

17.9b

Counts

205 → 34

Alt Table

Status	Error	Program
	60.7b	(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (log.f64 d))))
	61.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (+.f64 (log.f64 2) (log.f64 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 w) (log.f64 (.f64 h (pow.f64 M 2))))) (+.f64 (.f64 (log.f64 d) 2) (log.f64 c0))))))
	34.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	29.1b	(.f64 1/4 (/.f64 (.f64 (.f64 D (.f64 (*.f64 M M) h)) (/.f64 D d)) d))
	34.0b	(.f64 1/4 (/.f64 (expm1.f64 (log1p.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)))) d))
	34.0b	(.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))))
	28.9b	(.f64 1/4 (/.f64 (.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 D (cbrt.f64 d))) d))
	33.8b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (expm1.f64 (log1p.f64 (/.f64 (*.f64 D D) d)))) d))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (.f64 d d) c0)) -1/2))))
	31.4b	(.f64 1/4 (/.f64 (.f64 h (.f64 (.f64 M M) (/.f64 (*.f64 D D) d))) d))
	29.2b	(.f64 1/4 (.f64 (.f64 (.f64 M M) h) (*.f64 (/.f64 D d) (/.f64 D d))))
	61.4b	(.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)))))
	30.2b	(.f64 1/4 (/.f64 (.f64 (.f64 (.f64 h M) M) (/.f64 (*.f64 D D) d)) d))
	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)))))
	29.5b	(.f64 1/4 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 D d))))
	46.4b	(.f64 1/4 (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) (/.f64 (.f64 D D) d)) d))
	36.2b	(.f64 1/4 (/.f64 (log.f64 (exp.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)))) d))
	36.8b	(.f64 1/4 (cbrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 M M) h) 3) (pow.f64 (/.f64 d D) 6))))
	38.0b	(log.f64 (exp.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))))
	60.1b	(.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)))))
	56.1b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 (/.f64 (.f64 D D) d)))) d))
	58.9b	(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))))
	47.1b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (neg.f64 (log.f64 (/.f64 d h))))) d))
	56.0b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	51.6b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	62.4b	(.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)))))
	61.5b	(.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))))))
	51.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (neg.f64 (log.f64 (/.f64 (*.f64 d d) h))))))
	29.6b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 D (/.f64 d D))) d))
	49.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (sqrt.f64 M) 2) (.f64 (pow.f64 (sqrt.f64 M) 2) h))) (pow.f64 d 2)))
	61.5b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (log.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (*.f64 (log.f64 d) 2) (log.f64 c0))))))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (cbrt.f64 (pow.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)))) 3)))
	63.6b	(exp.f64 (+.f64 (log.f64 (/.f64 c0 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2)))) (log.f64 (.f64 (pow.f64 d 2) c0))))))
	47.1b	(.f64 1/4 (/.f64 (.f64 (.f64 (.f64 h (*.f64 M M)) (/.f64 D (sqrt.f64 d))) (/.f64 D (sqrt.f64 d))) d))

Compiler

Compiled 4949 to 1651 computations (66.6% saved)

regimes2.4s (10.9%)

Accuracy

Total 8.8b remaining (32.7%)

Threshold costs 0b (0%)

Counts

133 → 3

Compiler

Compiled 43808 to 30764 computations (29.8% saved)

bsearch291.0ms (1.3%)

Steps

Iters	Range		Point
5	1.3571109714240536e+127	2.8310683699165476e+127	2.795396578891542e+127
6	-1.783784929360231e+148	-1.429679448552213e+147	-1.7477617212624623e+148

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
5×	`+-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	45	103
1	61	103
2	66	103
3	69	103
4	70	103
5	70	103

end496.0ms (2.3%)

Compiler: Compiled 1148 to 762 computations (33.6% saved)

Details

analyze2.8s (13%)

sample9.6s (44%)

simplify42.0ms (0.2%)

prune5.0ms (0%)

localize19.0ms (0.1%)

series1.1s (5%)

rewrite104.0ms (0.5%)

simplify314.0ms (1.4%)

prune638.0ms (2.9%)

localize18.0ms (0.1%)

series632.0ms (2.9%)

rewrite207.0ms (1%)

simplify322.0ms (1.5%)

prune720.0ms (3.3%)

localize10.0ms (0%)

series325.0ms (1.5%)

rewrite52.0ms (0.2%)

simplify155.0ms (0.7%)

prune524.0ms (2.4%)

localize10.0ms (0%)

series210.0ms (1%)

rewrite40.0ms (0.2%)

simplify153.0ms (0.7%)

prune590.0ms (2.7%)

regimes2.4s (10.9%)

bsearch291.0ms (1.3%)

simplify5.0ms (0%)

end496.0ms (2.3%)

Profiling