Details

analyze2.7s (11.3%)

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)

sample11.7s (48.8%)

Results

3.1s	14723×	body	128	invalid
2.7s	2258×	body	8192	exit
2.2s	2230×	body	4096	valid
1.4s	1186×	body	8192	valid
1.0s	1311×	body	2048	valid
513.0ms	2443×	body	128	valid
430.0ms	652×	body	1024	valid
150.0ms	291×	body	512	valid
49.0ms	143×	body	256	valid
24.0ms	31×	body	2048	invalid
15.0ms	25×	body	1024	invalid
9.0ms	19×	body	512	invalid
5.0ms	4×	body	4096	invalid
3.0ms	10×	body	256	invalid

Compiler

Compiled 117 to 43 computations (63.2% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

60.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.1b	(.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)))))
▶	61.3b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))

Status

Error

Program

62.1b

(*.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)))))

▶

61.3b

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

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.5b	(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 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)))))
✓	19.2b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	32.1b	(+.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))))

series1.3s (5.3%)

Counts

4 → 276

Calls

4 calls:

494.0ms	(.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)))))
314.0ms	(+.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))))
276.0ms	(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)))
190.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite144.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-cbrt-cube_binary64`
82×	`add-exp-log_binary64`
43×	`cbrt-unprod_binary64`
43×	`prod-exp_binary64`
17×	`cbrt-undiv_binary64`

Counts

4 → 124

Calls

4 calls:

44.0ms	(.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)))))
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)))
12.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

simplify302.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

550×	`associate-/r*_binary64`
531×	`associate-/l*_binary64`
317×	`associate-*l/_binary64`
229×	`fma-def_binary64`
172×	`*-commutative_binary64`

Counts

400 → 312

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	537	24212
1	1649	21889
2	5007	21889

prune774.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	423	9	432
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	424	10	434

Error

30.6b

Counts

434 → 10

Alt Table

Status	Error	Program
	60.3b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
	61.3b	(.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)))))))
	43.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	62.1b	(.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)))))
▶	35.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	50.0b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	61.3b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (cbrt.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))))))
	61.3b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 c0 (/.f64 (.f64 (.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)))))

Compiler

Compiled 30725 to 7965 computations (74.1% saved)

localize10.0ms (0%)

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)))
✓	8.2b	(*.f64 (pow.f64 M 2) h)
✓	11.2b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	20.0b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series331.0ms (1.4%)

Counts

4 → 72

Calls

4 calls:

161.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
131.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
30.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
8.0ms	(*.f64 (pow.f64 M 2) h)

rewrite52.0ms (0.2%)

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:

12.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
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)

simplify146.0ms (0.6%)

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

prune499.0ms (2.1%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	210	21	231
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	213	28	241

Error

22.3b

Counts

241 → 28

Alt Table

Status	Error	Program
	62.1b	(.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)))))
▶	31.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	51.5b	(*.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)))))
	51.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 M (sqrt.f64 h)) (*.f64 M (sqrt.f64 h)))) (pow.f64 d 2)))
	57.3b	(.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)))))
	50.0b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	52.3b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 (sqrt.f64 d) 2)) (pow.f64 (sqrt.f64 d) 2)))
	61.3b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	49.6b	(.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)))
	60.1b	(.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)))))
	60.3b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
	60.8b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	61.3b	(.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)))))))
	35.9b	(.f64 1/4 (/.f64 1 (/.f64 (pow.f64 d 2) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.1b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	58.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 c0 (/.f64 (.f64 (.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)))))
	58.9b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	34.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	35.1b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 (pow.f64 d 2) (.f64 (pow.f64 M 2) h))))
	57.8b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	36.3b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	33.8b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	32.6b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) (.f64 d (cbrt.f64 d)))) (pow.f64 (cbrt.f64 d) 2)))
	34.5b	(.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)))
	54.7b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	31.4b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))

Compiler

Compiled 6766 to 4204 computations (37.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.6b	(/.f64 (.f64 h (.f64 M M)) d)
✓	8.2b	(/.f64 (*.f64 D D) d)
✓	8.2b	(.f64 h (.f64 M M))
✓	10.8b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series171.0ms (0.7%)

Counts

4 → 132

Calls

4 calls:

127.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
25.0ms	(/.f64 (.f64 h (.f64 M M)) d)
10.0ms	(/.f64 (*.f64 D D) d)
8.0ms	(.f64 h (.f64 M M))

rewrite34.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-cbrt-cube_binary64`
77×	`add-exp-log_binary64`
32×	`cbrt-unprod_binary64`
32×	`prod-exp_binary64`
22×	`cbrt-undiv_binary64`

Counts

4 → 123

Calls

4 calls:

10.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
6.0ms	(.f64 h (.f64 M M))
5.0ms	(/.f64 (.f64 h (.f64 M M)) d)
3.0ms	(/.f64 (*.f64 D D) d)

simplify139.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-/r*_binary64`
534×	`associate-/r/_binary64`
461×	`*-commutative_binary64`
309×	`log-div_binary64`
218×	`log-prod_binary64`

Counts

255 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	4137
1	400	3453
2	1576	3453
3	4069	3451
4	4865	3451
5	5026	3451

prune315.0ms (1.3%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	149	11	160
Fresh	11	16	27
Picked	1	0	1
Done	0	0	0
Total	161	27	188

Error

20.0b

Counts

188 → 27

Alt Table

Status	Error	Program
	27.9b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	62.1b	(.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)))))
	50.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (exp.f64 (+.f64 (log.f64 h) (log.f64 (.f64 M M)))) d)))
▶	27.7b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d))))
	57.8b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	51.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D (/.f64 D (sqrt.f64 d))) (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	57.3b	(.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)))))
	48.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) d)))
	60.1b	(.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)))))
	60.3b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
	60.8b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	61.3b	(.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)))))))
	35.9b	(.f64 1/4 (/.f64 1 (/.f64 (pow.f64 d 2) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.1b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	58.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 c0 (/.f64 (.f64 (.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)))))
	58.9b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	54.7b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	28.5b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	31.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 h (/.f64 (*.f64 M M) d))))
	28.7b	(.f64 1/4 (.f64 (.f64 D (/.f64 D d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	34.2b	(.f64 1/4 (exp.f64 (log.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))))
	32.6b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (.f64 D D) (.f64 d (cbrt.f64 d)))) (pow.f64 (cbrt.f64 d) 2)))
	61.3b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	31.3b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (.f64 (cbrt.f64 (/.f64 (.f64 h (.f64 M M)) d)) (cbrt.f64 (/.f64 (.f64 h (.f64 M M)) d)))) (cbrt.f64 (/.f64 (.f64 h (*.f64 M M)) d))))
	31.9b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (/.f64 1 d) (/.f64 (.f64 h (.f64 M M)) d))))

Compiler

Compiled 5291 to 1865 computations (64.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.3b	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
✓	5.2b	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))
	6.6b	(/.f64 (.f64 h (.f64 M M)) d)
	8.2b	(.f64 h (.f64 M M))

series1.5s (6.1%)

Counts

2 → 96

Calls

2 calls:

1.3s	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))
157.0ms	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))

rewrite57.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

187×	`add-exp-log_binary64`
153×	`add-cbrt-cube_binary64`
92×	`cbrt-unprod_binary64`
92×	`prod-exp_binary64`
58×	`cbrt-undiv_binary64`

Counts

2 → 143

Calls

2 calls:

16.0ms	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
11.0ms	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))

simplify156.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/r/_binary64`
350×	`associate-r_binary64`
307×	`associate-*l/_binary64`
307×	`times-frac_binary64`
295×	`associate-*r/_binary64`

Counts

239 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	7889
1	588	4982
2	2626	4964
3	4878	4964
4	4965	4964

prune640.0ms (2.7%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	257	9	266
Fresh	3	23	26
Picked	1	0	1
Done	0	0	0
Total	261	32	293

Error

17.9b

Counts

293 → 32

Alt Table

Status	Error	Program
	27.9b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	62.1b	(.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)))))
	50.3b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h (sqrt.f64 d))) (/.f64 (.f64 M M) (sqrt.f64 d)))))
	31.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 h (/.f64 (*.f64 M M) d))))
	57.8b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	51.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D (/.f64 D (sqrt.f64 d))) (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	57.3b	(.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)))))
	48.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) d)))
	28.7b	(.f64 1/4 (.f64 (.f64 D (/.f64 D d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	48.5b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (exp.f64 (+.f64 (log.f64 h) (log.f64 (*.f64 M M)))) d))))
	34.2b	(.f64 1/4 (exp.f64 (log.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))))
	27.8b	(.f64 1/4 (/.f64 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (.f64 h (.f64 M M)))) d))
	61.3b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	24.3b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 (.f64 h M) M) d))))
	60.1b	(.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)))))
	27.7b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d))) (cbrt.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d)))) (cbrt.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d))))))
	60.3b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
	60.8b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	61.3b	(.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)))))))
	35.9b	(.f64 1/4 (/.f64 1 (/.f64 (pow.f64 d 2) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.1b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	58.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 c0 (/.f64 (.f64 (.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)))))
	58.9b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	35.3b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (exp.f64 (log.f64 (/.f64 (.f64 h (.f64 M M)) d))))))
	54.7b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	28.5b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	31.9b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (/.f64 1 d) (/.f64 (.f64 h (.f64 M M)) d))))
	26.8b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 h (/.f64 D (cbrt.f64 d))) (/.f64 (.f64 M M) d))))
	26.7b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (/.f64 D d) h) (/.f64 (.f64 M M) (cbrt.f64 d)))))
	27.7b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) (.f64 (cbrt.f64 (cbrt.f64 d)) (cbrt.f64 (cbrt.f64 d)))) (.f64 (/.f64 (cbrt.f64 D) (cbrt.f64 (cbrt.f64 d))) (/.f64 (.f64 h (*.f64 M M)) d)))))

Compiler

Compiled 9462 to 2140 computations (77.4% saved)

regimes2.5s (10.4%)

Accuracy

Total 6.1b remaining (25.8%)

Threshold costs 0b (0%)

Counts

168 → 3

Compiler

Compiled 60405 to 35778 computations (40.8% saved)

bsearch10.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	108
1	45	108
2	45	108

end471.0ms (2%)

Compiler: Compiled 1212 to 687 computations (43.3% saved)

Details

analyze2.7s (11.3%)

sample11.7s (48.8%)

simplify41.0ms (0.2%)

prune5.0ms (0%)

localize20.0ms (0.1%)

series1.3s (5.3%)

rewrite144.0ms (0.6%)

simplify302.0ms (1.3%)

prune774.0ms (3.2%)

localize10.0ms (0%)

series331.0ms (1.4%)

rewrite52.0ms (0.2%)

simplify146.0ms (0.6%)

prune499.0ms (2.1%)

localize12.0ms (0.1%)

series171.0ms (0.7%)

rewrite34.0ms (0.1%)

simplify139.0ms (0.6%)

prune315.0ms (1.3%)

localize14.0ms (0.1%)

series1.5s (6.1%)

rewrite57.0ms (0.2%)

simplify156.0ms (0.7%)

prune640.0ms (2.7%)

regimes2.5s (10.4%)

bsearch10.0ms (0%)

simplify4.0ms (0%)

end471.0ms (2%)

Profiling