Details

analyze2.7s (14.6%)

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)

sample218.0ms (1.2%)

Algorithm

1×

intervals

Results

47.0ms	374×	body	128	nan
34.0ms	56×	body	4096	valid
33.0ms	43×	body	8192	valid
23.0ms	47×	body	2048	valid
12.0ms	117×	body	128	invalid
9.0ms	22×	body	1024	valid
8.0ms	77×	body	128	valid
2.0ms	8×	body	512	valid
1.0ms	3×	body	2048	invalid
1.0ms	2×	body	1024	invalid
1.0ms	3×	body	256	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify45.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
518×	`distribute-neg-frac_binary64`
416×	`fma-def_binary64`
304×	`associate-/l*_binary64`
217×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	78
1	64	74
2	296	74
3	3103	67
4	4218	67
5	5365	67

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

58.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.1b	(.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)))))
▶	58.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))

Status

Error

Program

61.1b

(*.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)))))

▶

58.7b

(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))
✓	14.0b	(.f64 (.f64 w h) (*.f64 D D))
✓	15.2b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	28.6b	(+.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))))

series842.0ms (4.6%)

Counts

4 → 240

Calls

4 calls:

327.0ms	(+.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))))
292.0ms	(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)))
199.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
23.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite94.0ms (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:

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))))
28.0ms	(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))

simplify282.0ms (1.5%)

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

prune564.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	410	7	417
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	411	8	419

Error

36.5b

Counts

419 → 8

Alt Table

Status	Error	Program
	50.7b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	61.1b	(.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)))))
	58.7b	(.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)))))))
	60.1b	(.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)))))
	60.0b	(.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)))))
	59.3b	(.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)))))
▶	42.4b	(.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))))
	59.1b	(.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 27669 to 6375 computations (77% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.6b	(*.f64 h (pow.f64 M 2))
✓	11.8b	(.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))))
✓	14.6b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
✓	15.7b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))

series626.0ms (3.4%)

Counts

4 → 156

Calls

4 calls:

301.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
252.0ms	(.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))))
10.0ms	(*.f64 h (pow.f64 M 2))

rewrite191.0ms (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:

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))))
10.0ms	(/.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 h (pow.f64 M 2))

simplify406.0ms (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

prune653.0ms (3.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	309	8	317
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	311	14	325

Error

28.3b

Counts

325 → 14

Alt Table

Status	Error	Program
	60.1b	(.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)))))
	41.0b	(/.f64 (.f64 c0 (.f64 1/2 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))))) (.f64 (.f64 2 w) (.f64 (pow.f64 d 2) c0)))
	60.0b	(.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)))))
	40.2b	(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)))
	41.6b	(.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))))
	62.3b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.f64 2 w))) (+.f64 (log.f64 1/2) (-.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))))))
	61.1b	(.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)))))
	58.7b	(.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)))))))
	42.2b	(.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))))
	61.6b	(.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))))))
	59.3b	(.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)))))
	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))))
▶	35.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	59.1b	(.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 12924 to 7819 computations (39.5% 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)))
✓	8.6b	(*.f64 (pow.f64 M 2) h)
✓	14.6b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	14.9b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series340.0ms (1.9%)

Counts

4 → 72

Calls

4 calls:

159.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
137.0ms	(/.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)

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))
10.0ms	(.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)

simplify150.0ms (0.8%)

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

prune438.0ms (2.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	217	14	231
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	223	22	245

Error

20.6b

Counts

245 → 22

Alt Table

Status	Error	Program
▶	32.8b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	36.0b	(.f64 1/4 (.f64 (.f64 D D) (/.f64 (.f64 h (.f64 M M)) (.f64 d d))))
	61.1b	(.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)))))
	57.2b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	56.4b	(.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)))
	58.7b	(.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)))))))
	61.3b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	57.2b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	51.8b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	40.2b	(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)))
	33.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	41.6b	(.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))))
	49.2b	(*.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	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))))
	35.6b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	34.3b	(.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 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)))))
	33.1b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	34.4b	(.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)))
	59.3b	(.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)))))
	33.9b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	59.1b	(.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 6458 to 3962 computations (38.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
✓	6.2b	(.f64 D (.f64 (pow.f64 M 2) h))
	8.6b	(*.f64 (pow.f64 M 2) h)
✓	14.9b	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))

series185.0ms (1%)

Counts

3 → 100

Calls

3 calls:

128.0ms	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))
33.0ms	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
24.0ms	(.f64 D (.f64 (pow.f64 M 2) h))

rewrite27.0ms (0.1%)

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))

simplify120.0ms (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

prune372.0ms (2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	169	12	181
Fresh	7	14	21
Picked	1	0	1
Done	0	0	0
Total	177	26	203

Error

17.6b

Counts

203 → 26

Alt Table

Status	Error	Program
	35.6b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	27.7b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))
	36.0b	(.f64 1/4 (.f64 (.f64 D D) (/.f64 (.f64 h (.f64 M M)) (.f64 d d))))
	61.1b	(.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)))))
	57.2b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	35.9b	(.f64 1/4 (exp.f64 (log.f64 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))))
	58.7b	(.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)))))))
	61.3b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	57.2b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	30.6b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) 2) (.f64 h (pow.f64 (cbrt.f64 M) 2))))) (pow.f64 d 2)))
	59.3b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 D) (+.f64 (log.f64 D) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h)))) (log.f64 (pow.f64 d 2)))))
	60.1b	(.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)))))
	30.0b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 M (*.f64 h M)))) (pow.f64 d 2)))
	51.8b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	40.2b	(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)))
	32.2b	(.f64 1/4 (/.f64 (.f64 (.f64 D (.f64 h (.f64 M M))) (/.f64 D (.f64 (cbrt.f64 (.f64 d d)) (cbrt.f64 (.f64 d d))))) (cbrt.f64 (pow.f64 d 2))))
	59.3b	(.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)))))
	47.7b	(.f64 1/4 (.f64 (/.f64 D (pow.f64 (sqrt.f64 d) 2)) (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))
	59.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	29.8b	(.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))))
	41.6b	(.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))))
	33.1b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	31.2b	(.f64 1/4 (/.f64 (.f64 D (.f64 (.f64 D (pow.f64 M 2)) h)) (pow.f64 d 2)))
	48.2b	(.f64 1/4 (/.f64 (.f64 D (cbrt.f64 (.f64 (.f64 (.f64 D D) D) (.f64 (.f64 (.f64 (pow.f64 M 2) (pow.f64 M 2)) (pow.f64 M 2)) (.f64 (.f64 h h) h))))) (pow.f64 d 2)))
	30.5b	(.f64 1/4 (/.f64 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) d) d))
	29.8b	(.f64 1/4 (/.f64 (.f64 (.f64 D (.f64 h (.f64 M M))) (/.f64 D (.f64 d (cbrt.f64 d)))) (pow.f64 (cbrt.f64 d) 2)))

Compiler

Compiled 4641 to 2639 computations (43.1% saved)

regimes2.4s (13%)

Accuracy

Total 6.2b remaining (24.3%)

Threshold costs 0b (0%)

Counts

154 → 2

Compiler

Compiled 67605 to 38453 computations (43.1% saved)

bsearch9.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	53
1	33	53
2	33	53

end1.0ms (0%)

Compiler: Compiled 42 to 25 computations (40.5% saved)

sample7.6s (41.3%)

Algorithm

1×

intervals

Results

1.6s	2121×	body	4096	valid
1.4s	11869×	body	128	nan
997.0ms	1177×	body	8192	valid
653.0ms	1239×	body	2048	valid
452.0ms	4036×	body	128	invalid
331.0ms	2425×	body	128	valid
261.0ms	591×	body	1024	valid
96.0ms	296×	body	512	valid
40.0ms	151×	body	256	valid
32.0ms	39×	body	512	invalid
29.0ms	58×	body	2048	invalid
23.0ms	47×	body	1024	invalid
4.0ms	6×	body	8192	exit
4.0ms	19×	body	256	invalid
4.0ms	6×	body	4096	invalid

Compiler

Compiled 938 to 552 computations (41.2% saved)

Details

analyze2.7s (14.6%)

sample218.0ms (1.2%)

simplify45.0ms (0.2%)

prune5.0ms (0%)

localize18.0ms (0.1%)

series842.0ms (4.6%)

rewrite94.0ms (0.5%)

simplify282.0ms (1.5%)

prune564.0ms (3.1%)

localize16.0ms (0.1%)

series626.0ms (3.4%)

rewrite191.0ms (1%)

simplify406.0ms (2.2%)

prune653.0ms (3.6%)

localize9.0ms (0.1%)

series340.0ms (1.9%)

rewrite56.0ms (0.3%)

simplify150.0ms (0.8%)

prune438.0ms (2.4%)

localize9.0ms (0.1%)

series185.0ms (1%)

rewrite27.0ms (0.1%)

simplify120.0ms (0.7%)

prune372.0ms (2%)

regimes2.4s (13%)

bsearch9.0ms (0%)

simplify3.0ms (0%)

end1.0ms (0%)

sample7.6s (41.3%)

Profiling