Details

analyze2.6s (13.1%)

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)

sample273.0ms (1.4%)

Algorithm

1×

intervals

Results

39.0ms	61×	body	4096	valid
37.0ms	348×	body	128	nan
29.0ms	38×	body	8192	valid
23.0ms	47×	body	2048	valid
15.0ms	135×	body	128	invalid
9.0ms	79×	body	128	valid
7.0ms	17×	body	1024	valid
3.0ms	9×	body	512	valid
1.0ms	5×	body	256	valid
1.0ms	2×	body	512	invalid
1.0ms	1×	body	4096	invalid
0.0ms	1×	body	2048	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify44.0ms (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

61.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 (.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))
▶	61.5b	(.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

62.7b

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

▶

61.5b

(*.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)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.4b	(.f64 (.f64 w h) (*.f64 D D))
✓	14.8b	(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)))
✓	18.7b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	28.2b	(+.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))))

series832.0ms (4.2%)

Counts

4 → 240

Calls

4 calls:

309.0ms	(+.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))))
301.0ms	(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)))
198.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
23.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite93.0ms (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:

36.0ms	(+.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)))
11.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
5.0ms	(.f64 (.f64 w h) (*.f64 D D))

simplify267.0ms (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

prune878.0ms (4.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	408	9	417
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	409	10	419

Error

37.4b

Counts

419 → 10

Alt Table

Status	Error	Program
	51.2b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	61.5b	(.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)))))))
	60.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	61.8b	(.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)))))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 w (.f64 h (.f64 D D)))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
▶	43.0b	(.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))))
	61.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	62.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 (.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))
	63.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (sqrt.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))))) (sqrt.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)))))))
	61.8b	(.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))))))

Compiler

Compiled 27927 to 6493 computations (76.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.7b	(*.f64 (pow.f64 d 2) c0)
✓	10.4b	(.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))))
✓	14.8b	(.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))

series628.0ms (3.2%)

Counts

4 → 144

Calls

4 calls:

297.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
262.0ms	(.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))))
59.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
9.0ms	(*.f64 (pow.f64 d 2) c0)

rewrite202.0ms (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:

24.0ms	(.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 (pow.f64 d 2) c0)

simplify317.0ms (1.6%)

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

prune835.0ms (4.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	306	11	317
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	308	19	327

Error

27.8b

Counts

327 → 19

Alt Table

Status	Error	Program
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 w (.f64 h (.f64 D D)))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	60.4b	(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))))))
	43.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (/.f64 1 (.f64 (pow.f64 d 2) c0)))))
	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 d (.f64 d c0)))))
	43.6b	(exp.f64 (log.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (.f64 d d) c0)) (*.f64 (/.f64 c0 w) 1/4))))
	51.2b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	61.5b	(.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)))))))
	40.9b	(.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))))
	60.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	61.8b	(.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)))))
	57.8b	(.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))))))
	61.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	43.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 D 2)) (cbrt.f64 (pow.f64 D 2))) (.f64 (cbrt.f64 (pow.f64 D 2)) (.f64 w (.f64 h (pow.f64 M 2))))) (*.f64 (pow.f64 d 2) c0))))
	41.5b	(.f64 (/.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) 2) (.f64 (/.f64 (cbrt.f64 c0) w) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0)))))
	60.7b	(.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) (.f64 (log.f64 M) 2))))) (*.f64 (pow.f64 d 2) c0))))
	63.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (sqrt.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))))) (sqrt.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)))))))
▶	34.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	61.8b	(.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))))))
	40.3b	(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)))

Compiler

Compiled 13366 to 8091 computations (39.5% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	7.6b	(*.f64 (pow.f64 M 2) h)
✓	14.9b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	15.1b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series209.0ms (1.1%)

Counts

3 → 40

Calls

3 calls:

165.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
35.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite36.0ms (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:

11.0ms	(/.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)

simplify123.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-*l/_binary64`
391×	`associate-/l/_binary64`
373×	`*-commutative_binary64`
370×	`associate-*r/_binary64`
310×	`fma-def_binary64`

Counts

173 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	3095
1	332	2730
2	1361	2677
3	4128	2571
4	4913	2571
5	5086	2571

prune438.0ms (2.2%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	143	17	160
Fresh	10	8	18
Picked	1	0	1
Done	0	0	0
Total	154	25	179

Error

20.9b

Counts

179 → 25

Alt Table

Status	Error	Program
	32.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 w (.f64 h (.f64 D D)))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	33.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	32.5b	(.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 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)))))
	61.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	48.2b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (sqrt.f64 M) 2) (.f64 h M))) (pow.f64 d 2)))
	57.7b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	36.6b	(.f64 1/4 (exp.f64 (log.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))))
	61.5b	(.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)))))))
	40.9b	(.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))))
	60.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	61.8b	(.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)))))
	33.6b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	55.0b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) (pow.f64 d 2)))
	55.9b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	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)))))
	63.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (sqrt.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))))) (sqrt.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)))))))
	59.1b	(.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))))
	32.2b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
▶	32.1b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	32.3b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	32.7b	(.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)))
	56.8b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 (pow.f64 M 2) h))) (.f64 (log.f64 d) 2))))
	40.3b	(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)))

Compiler

Compiled 5070 to 3097 computations (38.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d)) d)
✓	7.6b	(.f64 h (.f64 M M))
✓	8.2b	(/.f64 (*.f64 D D) d)
✓	14.0b	(.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d))

series216.0ms (1.1%)

Counts

4 → 144

Calls

4 calls:

127.0ms	(/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d)) d)
66.0ms	(.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d))
11.0ms	(.f64 h (.f64 M M))
11.0ms	(/.f64 (*.f64 D D) d)

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 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d)) d)
9.0ms	(.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d))
5.0ms	(/.f64 (*.f64 D D) d)
4.0ms	(.f64 h (.f64 M M))

simplify159.0ms (0.8%)

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

prune407.0ms (2.1%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	165	11	176
Fresh	8	16	24
Picked	1	0	1
Done	0	0	0
Total	174	27	201

Error

18.0b

Counts

201 → 27

Alt Table

Status	Error	Program
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 w (.f64 h (.f64 D D)))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	34.5b	(.f64 1/4 (exp.f64 (log.f64 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))))
	27.2b	(.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))
	32.5b	(.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 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)))))
	56.8b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (.f64 h (*.f64 M M))) (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (log.f64 d))))
	61.9b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	48.2b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (sqrt.f64 M) 2) (.f64 h M))) (pow.f64 d 2)))
	54.8b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (+.f64 (log.f64 h) (log.f64 (.f64 M M))) (log.f64 (/.f64 (*.f64 D D) d))) (log.f64 d))))
	61.5b	(.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)))))))
	29.8b	(.f64 1/4 (/.f64 (.f64 (.f64 (.f64 h M) M) (/.f64 (*.f64 D D) d)) d))
	52.8b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (neg.f64 (log.f64 (/.f64 d h))))) d))
	60.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	61.8b	(.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)))))
	33.6b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	55.0b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) (pow.f64 d 2)))
	28.3b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 D (/.f64 d D))) d))
	55.9b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	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)))))
	63.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (sqrt.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))))) (sqrt.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)))))))
	59.1b	(.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))))
	32.2b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	40.3b	(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)))
	28.2b	(.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))))
	31.3b	(.f64 1/4 (/.f64 (.f64 h (.f64 (.f64 M M) (/.f64 (*.f64 D D) d))) d))
	27.3b	(.f64 1/4 (/.f64 (.f64 (.f64 D (.f64 (*.f64 M M) h)) (/.f64 D d)) d))
	28.6b	(.f64 1/4 (.f64 (.f64 (.f64 M M) h) (*.f64 (/.f64 D d) (/.f64 D d))))

Compiler

Compiled 4853 to 1511 computations (68.9% saved)

regimes3.2s (16.2%)

Accuracy

Total 8.5b remaining (31.5%)

Threshold costs 0b (0%)

Counts

190 → 3

Compiler

Compiled 81128 to 47045 computations (42% saved)

bsearch341.0ms (1.7%)

Steps

Iters	Range		Point
9	7.644969832799406e+121	5.1265530098037647e+126	5.084131809070544e+126
6	-1.2314992942706056e+161	-1.9004495898190025e+160	-1.93057971646278e+160

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	100
1	57	100
2	62	100
3	64	100
4	65	100
5	65	100

end1.0ms (0%)

Compiler: Compiled 71 to 47 computations (33.8% saved)

sample7.6s (38.2%)

Algorithm

1×

intervals

Results

1.5s	2165×	body	4096	valid
1.4s	11968×	body	128	nan
1.0s	1116×	body	8192	valid
679.0ms	1219×	body	2048	valid
447.0ms	4041×	body	128	invalid
262.0ms	2432×	body	128	valid
259.0ms	612×	body	1024	valid
97.0ms	319×	body	512	valid
29.0ms	137×	body	256	valid
27.0ms	53×	body	2048	invalid
25.0ms	63×	body	1024	invalid
13.0ms	44×	body	512	invalid
7.0ms	11×	body	4096	invalid
4.0ms	6×	body	8192	exit
3.0ms	15×	body	256	invalid

Compiler

Compiled 1044 to 597 computations (42.8% saved)

Details

analyze2.6s (13.1%)

sample273.0ms (1.4%)

simplify44.0ms (0.2%)

prune5.0ms (0%)

localize21.0ms (0.1%)

series832.0ms (4.2%)

rewrite93.0ms (0.5%)

simplify267.0ms (1.4%)

prune878.0ms (4.4%)

localize20.0ms (0.1%)

series628.0ms (3.2%)

rewrite202.0ms (1%)

simplify317.0ms (1.6%)

prune835.0ms (4.2%)

localize10.0ms (0%)

series209.0ms (1.1%)

rewrite36.0ms (0.2%)

simplify123.0ms (0.6%)

prune438.0ms (2.2%)

localize12.0ms (0.1%)

series216.0ms (1.1%)

rewrite40.0ms (0.2%)

simplify159.0ms (0.8%)

prune407.0ms (2.1%)

regimes3.2s (16.2%)

bsearch341.0ms (1.7%)

simplify5.0ms (0%)

end1.0ms (0%)

sample7.6s (38.2%)

Profiling