Details

analyze2.7s (13.7%)

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)

sample9.5s (47.9%)

Results

3.3s	16117×	body	128	invalid
2.2s	2184×	body	4096	valid
1.4s	1229×	body	8192	valid
1.1s	1332×	body	2048	valid
588.0ms	2425×	body	128	valid
449.0ms	657×	body	1024	valid
130.0ms	271×	body	512	valid
53.0ms	158×	body	256	valid
43.0ms	50×	body	2048	invalid
35.0ms	54×	body	1024	invalid
20.0ms	43×	body	512	invalid
16.0ms	13×	body	4096	invalid
12.0ms	10×	body	8192	exit
5.0ms	16×	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

60.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.3b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 (.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))
▶	60.3b	(.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)))))

Status

Error

Program

62.3b

(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 c0 (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 c0 (*.f64 w h)) (*.f64 (*.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (*.f64 w h)))) (*.f64 M M)))))

▶

60.3b

(*.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)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.0b	(.f64 (.f64 w h) (*.f64 D D))
✓	13.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))
✓	16.1b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	27.2b	(+.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))))

series816.0ms (4.1%)

Counts

4 → 240

Calls

4 calls:

315.0ms	(+.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))))
287.0ms	(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)))
193.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
21.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite108.0ms (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:

46.0ms	(+.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))))
29.0ms	(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)))
6.0ms	(.f64 (.f64 w h) (*.f64 D D))

simplify319.0ms (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

prune443.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	413	4	417
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	414	5	419

Error

35.8b

Counts

419 → 5

Alt Table

Status	Error	Program
	60.8b	(.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 w h)) (/.f64 (.f64 d d) (.f64 D D)))) (.f64 M M)))))
	62.3b	(.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)))))
▶	41.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	51.3b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))

Compiler

Compiled 27221 to 6237 computations (77.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.5b	(*.f64 h (pow.f64 M 2))
✓	13.1b	(.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))))
✓	13.6b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
✓	17.3b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))

series793.0ms (4%)

Counts

4 → 156

Calls

4 calls:

421.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
273.0ms	(.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))))
89.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
9.0ms	(*.f64 h (pow.f64 M 2))

rewrite261.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

1737×	`add-exp-log_binary64`
1266×	`prod-exp_binary64`
388×	`div-exp_binary64`
236×	`add-cbrt-cube_binary64`
201×	`pow-exp_binary64`

Counts

4 → 404

Calls

4 calls:

21.0ms	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
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))))
7.0ms	(*.f64 h (pow.f64 M 2))

simplify430.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

560 → 317

Iterations

Useful iterations: 2 (0.0ms)

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

prune647.0ms (3.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	304	13	317
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	306	16	322

Error

28.0b

Counts

322 → 16

Alt Table

Status	Error	Program
	58.0b	(.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))))
	38.4b	(/.f64 (.f64 c0 (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0)))) (*.f64 2 w))
	59.9b	(.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))))
	39.2b	(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)))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	39.7b	(.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))))
	40.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (/.f64 (.f64 D D) (.f64 d d)) (.f64 w (.f64 (*.f64 M M) h))) c0)))
	60.0b	(.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))))))
	41.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (.f64 (pow.f64 D 2) w) (.f64 h (pow.f64 M 2))) (*.f64 (pow.f64 d 2) c0))))
	40.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 (.f64 h M) M))) (.f64 (pow.f64 d 2) c0))))
▶	34.6b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	42.5b	(cbrt.f64 (.f64 (.f64 (.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)))) (.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))))) (.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))))))
	62.3b	(.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)))))
	61.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (+.f64 (log.f64 2) (log.f64 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (log.f64 (.f64 h (pow.f64 M 2))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	58.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (exp.f64 (+.f64 (log.f64 h) (.f64 (log.f64 M) 2))))) (*.f64 (pow.f64 d 2) c0))))
	51.3b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))

Compiler

Compiled 12840 to 7987 computations (37.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	8.5b	(*.f64 (pow.f64 M 2) h)
✓	14.9b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	15.2b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series191.0ms (1%)

Counts

3 → 40

Calls

3 calls:

147.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
34.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
10.0ms	(*.f64 (pow.f64 M 2) h)

rewrite31.0ms (0.2%)

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:

8.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
7.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
4.0ms	(*.f64 (pow.f64 M 2) h)

simplify144.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

prune333.0ms (1.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	145	15	160
Fresh	12	3	15
Picked	1	0	1
Done	0	0	0
Total	158	18	176

Error

22.5b

Counts

176 → 18

Alt Table

Status	Error	Program
▶	32.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	55.3b	(.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)))))
	52.4b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	62.3b	(.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)))))
	61.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (+.f64 (log.f64 2) (log.f64 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (log.f64 (.f64 h (pow.f64 M 2))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	32.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	59.2b	(.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))))
	35.2b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	57.1b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	32.3b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	52.5b	(.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)))))
	56.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	32.4b	(.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))))
	34.7b	(.f64 1/4 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))) (cbrt.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)))) (cbrt.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)))) (pow.f64 d 2)))
	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)))
	50.7b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) (pow.f64 (sqrt.f64 d) 2)))
	32.5b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))

Compiler

Compiled 4336 to 2821 computations (34.9% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(/.f64 (.f64 h (.f64 M M)) d)
✓	8.5b	(.f64 h (.f64 M M))
✓	8.6b	(/.f64 (*.f64 D D) d)
✓	11.1b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series189.0ms (0.9%)

Counts

4 → 132

Calls

4 calls:

137.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
29.0ms	(/.f64 (.f64 h (.f64 M M)) d)
11.0ms	(.f64 h (.f64 M M))
11.0ms	(/.f64 (*.f64 D D) d)

rewrite39.0ms (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:

11.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
7.0ms	(/.f64 (.f64 h (.f64 M M)) d)
4.0ms	(.f64 h (.f64 M M))
4.0ms	(/.f64 (*.f64 D D) d)

simplify139.0ms (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

prune245.0ms (1.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	146	14	160
Fresh	10	7	17
Picked	1	0	1
Done	0	0	0
Total	157	21	178

Error

20.1b

Counts

178 → 21

Alt Table

Status	Error	Program
	29.3b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d D)) (/.f64 (.f64 h (.f64 M M)) d)))
	52.5b	(.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)))))
	32.2b	(.f64 1/4 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 D D) d)) (cbrt.f64 (/.f64 (.f64 D D) d))) (.f64 (cbrt.f64 (/.f64 (.f64 D D) d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	56.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	28.5b	(.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))))
	32.4b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (.f64 h (.f64 M M))) (/.f64 1 d)))
	48.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 D (sqrt.f64 d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	59.2b	(.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)))))
	55.5b	(.f64 1/4 (.f64 (/.f64 (*.f64 D D) d) (/.f64 (exp.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M)))) d)))
	55.2b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (/.f64 (.f64 h (.f64 M M)) d)))
	52.4b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	62.3b	(.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)))))
	61.8b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (+.f64 (log.f64 2) (log.f64 w))) (+.f64 (log.f64 1/2) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (log.f64 (.f64 h (pow.f64 M 2))))) (log.f64 (*.f64 (pow.f64 d 2) c0))))))
	32.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	30.9b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	59.4b	(.f64 1/4 (.f64 (/.f64 (*.f64 D D) d) (exp.f64 (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
	47.9b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	31.2b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (.f64 M M) (cbrt.f64 d))))
	30.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	49.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (exp.f64 (+.f64 (log.f64 h) (log.f64 (.f64 M M)))) d)))

Compiler

Compiled 4110 to 1210 computations (70.6% saved)

regimes1.8s (9.2%)

Accuracy

Total 8.0b remaining (29.3%)

Threshold costs 0b (0%)

Counts

127 → 3

Compiler

Compiled 42404 to 30248 computations (28.7% saved)

bsearch310.0ms (1.6%)

Steps

Iters	Range		Point
9	1.304055033352731e+97	4.770918980179075e+104	4.700540983952727e+104
5	-1.4585942510639312e-61	-4.897529042362598e-62	-1.3603938329136146e-61

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	70
1	41	70
2	41	70

end278.0ms (1.4%)

Compiler: Compiled 665 to 439 computations (34% saved)

Details

analyze2.7s (13.7%)

sample9.5s (47.9%)

simplify42.0ms (0.2%)

prune5.0ms (0%)

localize19.0ms (0.1%)

series816.0ms (4.1%)

rewrite108.0ms (0.5%)

simplify319.0ms (1.6%)

prune443.0ms (2.2%)

localize16.0ms (0.1%)

series793.0ms (4%)

rewrite261.0ms (1.3%)

simplify430.0ms (2.2%)

prune647.0ms (3.2%)

localize10.0ms (0.1%)

series191.0ms (1%)

rewrite31.0ms (0.2%)

simplify144.0ms (0.7%)

prune333.0ms (1.7%)

localize10.0ms (0%)

series189.0ms (0.9%)

rewrite39.0ms (0.2%)

simplify139.0ms (0.7%)

prune245.0ms (1.2%)

regimes1.8s (9.2%)

bsearch310.0ms (1.6%)

simplify3.0ms (0%)

end278.0ms (1.4%)

Profiling