Details

analyze2.8s (16.7%)

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)

sample233.0ms (1.4%)

Algorithm

1×

intervals

Results

46.0ms	413×	body	128	nan
45.0ms	66×	body	4096	valid
30.0ms	40×	body	8192	valid
22.0ms	40×	body	2048	valid
16.0ms	153×	body	128	invalid
13.0ms	71×	body	128	valid
8.0ms	20×	body	1024	valid
4.0ms	15×	body	512	valid
2.0ms	3×	body	2048	invalid
1.0ms	4×	body	256	valid
1.0ms	2×	body	1024	invalid
1.0ms	1×	body	8192	exit
1.0ms	3×	body	256	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify48.0ms (0.3%)

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

60.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	60.6b	(.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)))))
	62.5b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 (.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))

Status

Error

Program

▶

60.6b

(*.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)))))

62.5b

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

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	16.1b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
	16.1b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	16.1b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	28.3b	(+.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))))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-cbrt-cube_binary64`
71×	`add-exp-log_binary64`
39×	`cbrt-unprod_binary64`
39×	`prod-exp_binary64`
15×	`cbrt-undiv_binary64`

Counts

2 → 66

Calls

2 calls:

39.0ms

(+.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))))

10.0ms

(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))

series567.0ms (3.4%)

Counts

2 → 132

Calls

2 calls:

289.0ms

(+.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))))

278.0ms

(/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))

simplify199.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

755×	`times-frac_binary64`
423×	`associate-r_binary64`
416×	`associate-l_binary64`
381×	`fma-neg_binary64`
312×	`associate-/l*_binary64`

Counts

198 → 385

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	301	8443
1	852	7827
2	4872	7827
3	5187	7827

prune423.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	996	10	1006
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	998	10	1008

Error

32.8b

Counts

1008 → 10

Alt Table

Status	Error	Program
	40.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) (.f64 w h))) (.f64 (.f64 d d) c0))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
▶	37.9b	(.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))))
	50.2b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	63.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 (pow.f64 d 4) c0) (.f64 (pow.f64 D 4) (.f64 w h)))) (.f64 M M))))) (cbrt.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 (pow.f64 d 4) c0) (.f64 (pow.f64 D 4) (.f64 w h)))) (.f64 M M)))))) (cbrt.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 (pow.f64 d 4) c0) (.f64 (pow.f64 D 4) (.f64 w h)))) (*.f64 M M)))))))
	61.4b	(.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)))))
	61.4b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))))) (cbrt.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)))))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 d d)) (.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)))))
	61.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 1 (/.f64 (.f64 (.f64 w h) (.f64 D D)) (.f64 c0 (.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 17329 to 3781 computations (78.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.8b	(.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))))
✓	12.6b	(*.f64 (pow.f64 d 2) c0)
✓	14.6b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
✓	14.9b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))

rewrite111.0ms (0.7%)

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:

25.0ms	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
12.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
7.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
4.0ms	(*.f64 (pow.f64 d 2) c0)

series906.0ms (5.5%)

Counts

4 → 144

Calls

4 calls:

424.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
323.0ms	(.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))))
132.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
27.0ms	(*.f64 (pow.f64 d 2) c0)

simplify420.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

548 → 1085

Iterations

Useful iterations: 1 (0.0ms)

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

prune599.0ms (3.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	1074	11	1085
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	1075	20	1095

Error

24.4b

Counts

1095 → 20

Alt Table

Status	Error	Program
	40.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) (.f64 w h))) (.f64 (.f64 d d) c0))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	34.9b	(.f64 c0 (.f64 (/.f64 1/4 w) (/.f64 (.f64 (.f64 D D) (.f64 w (.f64 (.f64 M M) h))) (.f64 (*.f64 d d) c0))))
	59.1b	(.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))))))
	34.4b	(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)))
	35.5b	(.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))))
	63.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 (pow.f64 d 4) c0) (.f64 (pow.f64 D 4) (.f64 w h)))) (.f64 M M))))) (cbrt.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 (pow.f64 d 4) c0) (.f64 (pow.f64 D 4) (.f64 w h)))) (.f64 M M)))))) (cbrt.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 (pow.f64 d 4) c0) (.f64 (pow.f64 D 4) (.f64 w h)))) (*.f64 M M)))))))
	61.1b	(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))))) (+.f64 (log.f64 (pow.f64 d 2)) (log.f64 c0))))))
	61.4b	(.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)))))
	61.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 w) (+.f64 (log.f64 h) (.f64 (log.f64 M) 2))))) (*.f64 (pow.f64 d 2) c0))))
	61.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 1 (/.f64 (.f64 (.f64 w h) (.f64 D D)) (.f64 c0 (.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)))))
	37.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 d (.f64 d c0)))))
▶	31.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	50.2b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	38.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 (pow.f64 D 2) (pow.f64 d 2)) (/.f64 (.f64 w (.f64 h (pow.f64 M 2))) c0))))
	36.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) 2) (.f64 (pow.f64 (cbrt.f64 D) 2) (.f64 w (.f64 h (pow.f64 M 2))))) (*.f64 (pow.f64 d 2) c0))))
	61.4b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))))) (cbrt.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)))))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 d d)) (.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)))))
	51.3b	(.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 (sqrt.f64 d) 2) (.f64 d c0)))))

Compiler

Compiled 13374 to 8107 computations (39.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	7.2b	(*.f64 (pow.f64 M 2) h)
✓	13.1b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
✓	15.4b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

rewrite27.0ms (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 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
7.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
4.0ms	(*.f64 (pow.f64 M 2) h)

series269.0ms (1.6%)

Counts

3 → 40

Calls

3 calls:

170.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
72.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
27.0ms	(*.f64 (pow.f64 M 2) h)

simplify145.0ms (0.9%)

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 → 338

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 (2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	322	16	338
Fresh	12	7	19
Picked	1	0	1
Done	0	0	0
Total	335	23	358

Error

18.4b

Counts

358 → 23

Alt Table

Status	Error	Program
	28.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	30.8b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	46.2b	(.f64 1/4 (.f64 (/.f64 (pow.f64 D 2) (pow.f64 (sqrt.f64 d) 2)) (/.f64 (*.f64 (pow.f64 M 2) h) (pow.f64 (sqrt.f64 d) 2))))
▶	27.4b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	29.5b	(.f64 1/4 (.f64 (/.f64 (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))))
	59.1b	(.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))))))
	30.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	34.4b	(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)))
	61.4b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))))) (cbrt.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)))))
	59.5b	(.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))))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 d d)) (.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)))))
	28.8b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	57.5b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	61.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 1 (/.f64 (.f64 (.f64 w h) (.f64 D D)) (.f64 c0 (.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)))))
	29.4b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	58.2b	(.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)))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	28.3b	(.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)))
	52.4b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	47.7b	(*.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)))))
	55.6b	(.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)))))
	56.2b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))

Compiler

Compiled 4727 to 2973 computations (37.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
✓	6.0b	(.f64 D (.f64 (pow.f64 M 2) h))
	7.2b	(*.f64 (pow.f64 M 2) h)
✓	13.1b	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))

rewrite26.0ms (0.2%)

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:

9.0ms	(/.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))

series304.0ms (1.8%)

Counts

3 → 100

Calls

3 calls:

172.0ms	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))
72.0ms	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
59.0ms	(.f64 D (.f64 (pow.f64 M 2) h))

simplify131.0ms (0.8%)

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 → 383

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	3573
1	317	3183
2	1481	3183
3	4665	3158
4	5070	3158

prune364.0ms (2.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	454	8	462
Fresh	4	18	22
Picked	1	0	1
Done	0	0	0
Total	459	26	485

Error

16.7b

Counts

485 → 26

Alt Table

Status	Error	Program
	60.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	29.5b	(.f64 1/4 (.f64 (/.f64 (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))))
	59.1b	(.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))))))
	28.3b	(.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)))
	25.0b	(.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))))
	30.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	34.4b	(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)))
	52.4b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	26.4b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 M (*.f64 h M)))) (pow.f64 d 2)))
	59.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 D) (+.f64 (log.f64 D) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h)))) (*.f64 (log.f64 d) 2))))
	61.4b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (cbrt.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))))) (cbrt.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)))))
	59.5b	(.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))))
	26.7b	(.f64 1/4 (/.f64 (.f64 D (.f64 (.f64 D (pow.f64 M 2)) h)) (pow.f64 d 2)))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 d d)) (.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)))))
	57.5b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	61.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 1 (/.f64 (.f64 (.f64 w h) (.f64 D D)) (.f64 c0 (.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)))))
	29.4b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	56.2b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	23.3b	(.f64 1/4 (.f64 (/.f64 D d) (/.f64 (.f64 D (.f64 (pow.f64 M 2) h)) d)))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	28.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	22.6b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))
	55.4b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 (.f64 D (.f64 (pow.f64 M 2) h)))) (.f64 (log.f64 d) 2))))
	47.7b	(*.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)))))
	55.6b	(.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)))))
	29.0b	(.f64 1/4 (/.f64 (.f64 D (expm1.f64 (log1p.f64 (.f64 D (.f64 (pow.f64 M 2) h))))) (pow.f64 d 2)))

Compiler

Compiled 4522 to 2605 computations (42.4% saved)

regimes1.3s (7.6%)

Accuracy

Total 8.2b remaining (30.4%)

Threshold costs 0b (0%)

Compiler

Compiled 38631 to 24144 computations (37.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	16	22
2	16	22

end1.0ms (0%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

sample7.3s (44.2%)

Algorithm

1×

intervals

Results

1.4s	2151×	body	4096	valid
1.4s	12321×	body	128	nan
1.1s	1175×	body	8192	valid
676.0ms	1285×	body	2048	valid
470.0ms	4050×	body	128	invalid
286.0ms	604×	body	1024	valid
247.0ms	2356×	body	128	valid
91.0ms	298×	body	512	valid
30.0ms	131×	body	256	valid
24.0ms	49×	body	2048	invalid
23.0ms	55×	body	1024	invalid
10.0ms	17×	body	4096	invalid
9.0ms	32×	body	512	invalid
7.0ms	9×	body	8192	exit
5.0ms	23×	body	256	invalid

Compiler

Compiled 873 to 548 computations (37.2% saved)

Details

analyze2.8s (16.7%)

sample233.0ms (1.4%)

simplify48.0ms (0.3%)

prune5.0ms (0%)

localize23.0ms (0.1%)

rewrite59.0ms (0.4%)

series567.0ms (3.4%)

simplify199.0ms (1.2%)

prune423.0ms (2.6%)

localize18.0ms (0.1%)

rewrite111.0ms (0.7%)

series906.0ms (5.5%)

simplify420.0ms (2.5%)

prune599.0ms (3.6%)

localize10.0ms (0.1%)

rewrite27.0ms (0.2%)

series269.0ms (1.6%)

simplify145.0ms (0.9%)

prune333.0ms (2%)

localize10.0ms (0.1%)

rewrite26.0ms (0.2%)

series304.0ms (1.8%)

simplify131.0ms (0.8%)

prune364.0ms (2.2%)

regimes1.3s (7.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample7.3s (44.2%)

Profiling