Details

analyze2.6s (15%)

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)

sample233.0ms (1.3%)

Algorithm

1×

intervals

Results

71.0ms	74×	body	4096	valid
37.0ms	391×	body	128	nan
28.0ms	35×	body	8192	valid
16.0ms	34×	body	2048	valid
13.0ms	133×	body	128	invalid
8.0ms	21×	body	1024	valid
7.0ms	76×	body	128	valid
3.0ms	11×	body	512	valid
1.0ms	3×	body	1024	invalid
1.0ms	5×	body	256	valid
1.0ms	3×	body	512	invalid
1.0ms	1×	body	4096	invalid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify43.0ms (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

prune7.0ms (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

59.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.3b	(.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)))))
▶	59.8b	(.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 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))

Status

Error

Program

61.3b

(*.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)))))

▶

59.8b

(*.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 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
✓	12.3b	(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))
✓	16.0b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	29.5b	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))

series812.0ms (4.7%)

Counts

4 → 240

Calls

4 calls:

313.0ms	(+.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))))
283.0ms	(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)))
22.0ms	(.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))))
27.0ms	(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))

simplify263.0ms (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

prune615.0ms (3.5%)

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

36.2b

Counts

419 → 9

Alt Table

Status	Error	Program
	61.3b	(.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)))))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (exp.f64 (log.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)))))))
	60.0b	(.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 1 (.f64 (.f64 w h) (.f64 D D))))) (.f64 M M)))))
	52.8b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	61.7b	(.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))))))
	60.1b	(.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)))))
	60.7b	(.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))))
▶	43.6b	(.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))))
	59.2b	(.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 27659 to 6425 computations (76.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	9.6b	(*.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))))
✓	13.7b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
✓	17.6b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))

series599.0ms (3.4%)

Counts

4 → 144

Calls

4 calls:

281.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
248.0ms	(.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))))
11.0ms	(*.f64 (pow.f64 d 2) c0)

rewrite209.0ms (1.2%)

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))))
11.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
10.0ms	(*.f64 (pow.f64 d 2) c0)
7.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))

simplify328.0ms (1.9%)

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

prune733.0ms (4.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	304	13	317
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	305	21	326

Error

27.9b

Counts

326 → 21

Alt Table

Status	Error	Program
	59.3b	(.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))))))
	61.3b	(.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)))))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (exp.f64 (log.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)))))))
	59.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (log.f64 (.f64 w (.f64 h (pow.f64 M 2))))) (+.f64 (.f64 (log.f64 d) 2) (log.f64 c0))))))
	58.7b	(.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))))
	41.6b	(.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)))))
	62.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2))))) (.f64 (pow.f64 d 2) c0))))
	60.7b	(.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))))
	41.3b	(.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))))
	52.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (exp.f64 (log.f64 (.f64 (.f64 d d) c0))))))
	59.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.4b	(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))))))
	60.0b	(.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 1 (.f64 (.f64 w h) (.f64 D D))))) (.f64 M M)))))
	52.8b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	61.7b	(.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))))))
	60.1b	(.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)))))
▶	37.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	43.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))))
	43.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (.f64 (pow.f64 d 2) (*.f64 (cbrt.f64 c0) (cbrt.f64 c0))) (cbrt.f64 c0)))))
	59.1b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.f64 2 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 (log.f64 (pow.f64 d 2)) (log.f64 c0))))))
	40.7b	(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 13358 to 8203 computations (38.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	6.5b	(*.f64 (pow.f64 M 2) h)
✓	14.8b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
✓	18.1b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

series166.0ms (1%)

Counts

3 → 40

Calls

3 calls:

125.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
31.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite30.0ms (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))
6.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
4.0ms	(*.f64 (pow.f64 M 2) h)

simplify124.0ms (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

prune339.0ms (1.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	147	13	160
Fresh	10	10	20
Picked	1	0	1
Done	0	0	0
Total	158	23	181

Error

21.8b

Counts

181 → 23

Alt Table

Status	Error	Program
	61.3b	(.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)))))
	57.4b	(.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)))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (exp.f64 (log.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 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)))))
	56.9b	(.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)))))
	54.6b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	43.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))))
▶	34.2b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	35.3b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	57.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	41.3b	(.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))))
	52.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (exp.f64 (log.f64 (.f64 (.f64 d d) c0))))))
	36.7b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	49.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	60.0b	(.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 1 (.f64 (.f64 w h) (.f64 D D))))) (.f64 M M)))))
	36.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	60.7b	(.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))))
	54.1b	(.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)))))
	35.1b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	59.1b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.f64 2 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 (log.f64 (pow.f64 d 2)) (log.f64 c0))))))
	37.5b	(.f64 1/4 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 D 2)) (cbrt.f64 (pow.f64 D 2))) (.f64 (cbrt.f64 (pow.f64 D 2)) (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	34.7b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	40.7b	(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 4862 to 3048 computations (37.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d)) d)
✓	6.5b	(.f64 h (.f64 M M))
✓	8.2b	(/.f64 (*.f64 D D) d)
✓	15.6b	(.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d))

series217.0ms (1.2%)

Counts

4 → 144

Calls

4 calls:

131.0ms	(/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d)) d)
65.0ms	(.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d))
11.0ms	(/.f64 (*.f64 D D) d)
10.0ms	(.f64 h (.f64 M M))

rewrite41.0ms (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)
8.0ms	(.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) d))
6.0ms	(.f64 h (.f64 M M))
3.0ms	(/.f64 (*.f64 D D) d)

simplify155.0ms (0.9%)

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

prune320.0ms (1.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	162	14	176
Fresh	10	12	22
Picked	1	0	1
Done	0	0	0
Total	173	26	199

Error

18.3b

Counts

199 → 26

Alt Table

Status	Error	Program
	61.3b	(.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)))))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (exp.f64 (log.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)))))))
	30.1b	(.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))
	54.6b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	60.1b	(.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)))))
	32.5b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (cbrt.f64 d))) d))
	56.9b	(.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)))))
	42.4b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (exp.f64 (log.f64 (/.f64 (*.f64 D D) d)))) d))
	60.7b	(.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))))
	30.4b	(.f64 1/4 (.f64 (.f64 (.f64 M M) h) (*.f64 (/.f64 D d) (/.f64 D d))))
	32.4b	(.f64 1/4 (/.f64 (.f64 h (.f64 (.f64 M M) (/.f64 (*.f64 D D) d))) d))
	30.3b	(.f64 1/4 (/.f64 (.f64 (.f64 D (.f64 (*.f64 M M) h)) (/.f64 D d)) d))
	59.1b	(exp.f64 (+.f64 (-.f64 (log.f64 c0) (log.f64 (.f64 2 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 (log.f64 (pow.f64 d 2)) (log.f64 c0))))))
	32.7b	(.f64 1/4 (/.f64 (.f64 (.f64 (.f64 h M) M) (/.f64 (*.f64 D D) d)) d))
	59.8b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (+.f64 (log.f64 h) (log.f64 (.f64 M M))) (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d)))) d))
	36.5b	(.f64 1/4 (exp.f64 (log.f64 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))))
	51.4b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (neg.f64 (log.f64 (/.f64 d h))))) d))
	60.5b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (-.f64 (log.f64 (.f64 D D)) (log.f64 d))) (log.f64 d))))
	31.0b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (*.f64 D (/.f64 D d))) d))
	40.7b	(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)))
	54.4b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (neg.f64 (log.f64 (/.f64 (*.f64 d d) h))))))
	60.0b	(.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 1 (.f64 (.f64 w h) (.f64 D D))))) (.f64 M M)))))
	35.0b	(.f64 1/4 (/.f64 (.f64 h (.f64 M M)) (/.f64 d (/.f64 (.f64 D D) d))))
	43.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (expm1.f64 (log1p.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))))
	57.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	37.5b	(.f64 1/4 (/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 D 2)) (cbrt.f64 (pow.f64 D 2))) (.f64 (cbrt.f64 (pow.f64 D 2)) (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))

Compiler

Compiled 4764 to 1491 computations (68.7% saved)

regimes2.4s (13.5%)

Accuracy

Total 10.5b remaining (36.1%)

Threshold costs 0b (0%)

Counts

151 → 4

Compiler

Compiled 55639 to 36749 computations (34% saved)

bsearch297.0ms (1.7%)

Steps

Iters	Range	Point
6	3.8401860121048294e+164	1.5916618260978595e+165	1.5768310252267593e+165
4	8.414484226794673e-284	2.1314663574367696e-265	3.803592874752181e-271
9	-1.0636339006676033e-80	-1.6149291551029055e-88	-1.208739675252761e-87

Iters

Range

Point

3.8401860121048294e+164

1.5916618260978595e+165

1.5768310252267593e+165

8.414484226794673e-284

2.1314663574367696e-265

3.803592874752181e-271

-1.0636339006676033e-80

-1.6149291551029055e-88

-1.208739675252761e-87

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	118
1	55	118
2	55	118

end1.0ms (0%)

Compiler: Compiled 85 to 44 computations (48.2% saved)

sample6.8s (38.9%)

Algorithm

1×

intervals

Results

1.3s	2125×	body	4096	valid
1.2s	12085×	body	128	nan
919.0ms	1202×	body	8192	valid
624.0ms	1226×	body	2048	valid
439.0ms	4099×	body	128	invalid
257.0ms	2362×	body	128	valid
252.0ms	646×	body	1024	valid
86.0ms	305×	body	512	valid
25.0ms	134×	body	256	valid
25.0ms	64×	body	1024	invalid
22.0ms	44×	body	2048	invalid
11.0ms	40×	body	512	invalid
8.0ms	13×	body	4096	invalid
7.0ms	10×	body	8192	exit
2.0ms	9×	body	256	invalid

Compiler

Compiled 969 to 574 computations (40.8% saved)

Details

analyze2.6s (15%)

sample233.0ms (1.3%)

simplify43.0ms (0.2%)

prune7.0ms (0%)

localize18.0ms (0.1%)

series812.0ms (4.7%)

rewrite94.0ms (0.5%)

simplify263.0ms (1.5%)

prune615.0ms (3.5%)

localize16.0ms (0.1%)

series599.0ms (3.4%)

rewrite209.0ms (1.2%)

simplify328.0ms (1.9%)

prune733.0ms (4.2%)

localize11.0ms (0.1%)

series166.0ms (1%)

rewrite30.0ms (0.2%)

simplify124.0ms (0.7%)

prune339.0ms (1.9%)

localize12.0ms (0.1%)

series217.0ms (1.2%)

rewrite41.0ms (0.2%)

simplify155.0ms (0.9%)

prune320.0ms (1.8%)

regimes2.4s (13.5%)

bsearch297.0ms (1.7%)

simplify4.0ms (0%)

end1.0ms (0%)

sample6.8s (38.9%)

Profiling