Details

analyze2.7s (12.5%)

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)

sample9.0s (41.6%)

Results

3.1s	16371×	body	128	invalid
2.0s	2135×	body	4096	valid
1.5s	1238×	body	8192	valid
1.1s	1379×	body	2048	valid
478.0ms	2432×	body	128	valid
362.0ms	585×	body	1024	valid
167.0ms	342×	body	512	valid
52.0ms	145×	body	256	valid
49.0ms	64×	body	2048	invalid
38.0ms	61×	body	1024	invalid
15.0ms	17×	body	4096	invalid
15.0ms	31×	body	512	invalid
10.0ms	25×	body	256	invalid
4.0ms	4×	body	8192	exit

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify42.0ms (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

prune4.0ms (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

60.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	60.4b	(.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)))))
	63.1b	(.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)))))

Status

Error

Program

▶

60.4b

(*.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)))))

63.1b

(*.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)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.9b	(.f64 (.f64 w h) (*.f64 D D))
✓	13.5b	(.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)))))
✓	17.0b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	30.0b	(+.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))))

series1.1s (5%)

Counts

4 → 240

Calls

4 calls:

561.0ms	(.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)))))
302.0ms	(+.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))))
190.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
23.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite125.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`add-cbrt-cube_binary64`
94×	`add-exp-log_binary64`
51×	`cbrt-unprod_binary64`
51×	`prod-exp_binary64`
18×	`pow1_binary64`

Counts

4 → 130

Calls

4 calls:

46.0ms	(.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))))
12.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
6.0ms	(.f64 (.f64 w h) (*.f64 D D))

simplify360.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

488×	`associate-/r*_binary64`
478×	`associate-/l*_binary64`
460×	`fma-def_binary64`
295×	`associate-*l/_binary64`
278×	`associate-*r/_binary64`

Counts

370 → 279

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	477	18780
1	1465	16679
2	4886	16625
3	5160	16625

prune680.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	453	10	463
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	454	11	465

Error

29.0b

Counts

465 → 11

Alt Table

Status	Error	Program
▶	35.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (+.f64 (log.f64 d) (log.f64 d))) (log.f64 (.f64 (.f64 w h) (.f64 D D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	42.6b	(.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))))
	60.9b	(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))))
	61.6b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.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)))))
	50.9b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	60.4b	(.f64 (/.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) 2) (.f64 (/.f64 (cbrt.f64 c0) 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))))))
	60.5b	(/.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))
	63.9b	(exp.f64 (log.f64 (.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)))))
	63.1b	(.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)))))

Compiler

Compiled 31494 to 6969 computations (77.9% 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)))
✓	6.6b	(*.f64 (pow.f64 M 2) h)
✓	14.9b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	16.3b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series348.0ms (1.6%)

Counts

4 → 72

Calls

4 calls:

153.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
149.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
36.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite51.0ms (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:

10.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
7.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
7.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
4.0ms	(*.f64 (pow.f64 M 2) h)

simplify178.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

506×	`*-commutative_binary64`
444×	`associate-/l/_binary64`
380×	`fma-def_binary64`
373×	`associate-/r/_binary64`
294×	`log-prod_binary64`

Counts

277 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	5669
1	422	5071
2	1672	5018
3	3936	4789
4	5006	4789

prune436.0ms (2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	214	17	231
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	218	24	242

Error

20.6b

Counts

242 → 24

Alt Table

Status	Error	Program
▶	30.6b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	61.6b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	46.8b	(.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))))
	55.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	35.5b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	52.9b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	31.5b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.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)))))
	55.6b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	55.8b	(.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)))
	59.1b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	60.5b	(/.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))
	30.9b	(.f64 1/4 (/.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 (*.f64 D D) d)) d))
	53.6b	(.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))))
	63.9b	(exp.f64 (log.f64 (.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)))))
	58.6b	(.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))))
	60.9b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	56.7b	(.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))))
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (+.f64 (log.f64 d) (log.f64 d))) (log.f64 (.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)))))
	33.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	32.1b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	31.9b	(.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))))
	60.9b	(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))))
	63.1b	(.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)))))

Compiler

Compiled 6588 to 4082 computations (38% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.7b	(/.f64 (.f64 h (.f64 M M)) d)
✓	6.6b	(.f64 h (.f64 M M))
✓	7.2b	(/.f64 (*.f64 D D) d)
✓	12.5b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series386.0ms (1.8%)

Counts

4 → 132

Calls

4 calls:

133.0ms	(/.f64 (.f64 h (.f64 M M)) d)
131.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
112.0ms	(/.f64 (*.f64 D D) d)
9.0ms	(.f64 h (.f64 M M))

rewrite35.0ms (0.2%)

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

simplify174.0ms (0.8%)

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

prune301.0ms (1.4%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	149	11	160
Fresh	7	16	23
Picked	1	0	1
Done	0	0	0
Total	157	27	184

Error

18.3b

Counts

184 → 27

Alt Table

Status	Error	Program
	30.6b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 h (/.f64 (*.f64 M M) d))))
	27.4b	(.f64 1/4 (.f64 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 D (cbrt.f64 d))) (/.f64 (.f64 h (.f64 M M)) d)))
	26.0b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (+.f64 (log.f64 d) (log.f64 d))) (log.f64 (.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)))))
	61.6b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	55.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	35.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (exp.f64 (log.f64 (/.f64 (.f64 h (*.f64 M M)) d)))))
	35.5b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
▶	25.5b	(.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))))
	52.9b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	55.6b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	55.8b	(.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)))
	59.1b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	60.5b	(/.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))
	47.1b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	60.9b	(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))))
	28.9b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	63.9b	(exp.f64 (log.f64 (.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)))))
	60.9b	(*.f64 1/4 (exp.f64 (+.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d)) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
	27.4b	(.f64 1/4 (.f64 (.f64 D (/.f64 D d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	60.9b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	44.2b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	33.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.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)))))
	32.1b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	30.5b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	63.1b	(.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)))))

Compiler

Compiled 5255 to 1865 computations (64.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.6b	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	4.7b	(/.f64 (.f64 h (.f64 M M)) d)
	6.6b	(.f64 h (.f64 M M))
✓	7.2b	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))

series1.7s (7.6%)

Counts

2 → 96

Calls

2 calls:

1.5s	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))
172.0ms	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))

rewrite60.0ms (0.3%)

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:

17.0ms	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
13.0ms	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))

simplify152.0ms (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

prune502.0ms (2.3%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	256	10	266
Fresh	4	22	26
Picked	1	0	1
Done	0	0	0
Total	261	32	293

Error

17.2b

Counts

293 → 32

Alt Table

Status	Error	Program
	26.0b	(.f64 1/4 (.f64 D (/.f64 (.f64 D (/.f64 (.f64 (*.f64 M M) h) d)) d)))
	63.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (exp.f64 (-.f64 (+.f64 (log.f64 c0) (+.f64 (log.f64 d) (log.f64 d))) (log.f64 (.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)))))
	61.6b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	55.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	35.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (exp.f64 (log.f64 (/.f64 (.f64 h (*.f64 M M)) d)))))
	35.5b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	52.9b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	61.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.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)))))
	25.6b	(.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)))))
	33.5b	(.f64 1/4 (.f64 (sqrt.f64 (/.f64 (.f64 D (.f64 D (.f64 (.f64 M M) h))) (.f64 d d))) (sqrt.f64 (/.f64 (.f64 D (.f64 D (.f64 (.f64 M M) h))) (.f64 d d)))))
	32.1b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	24.4b	(.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)))))
	55.6b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	55.8b	(.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)))
	59.1b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	60.7b	(.f64 1/4 (exp.f64 (+.f64 (log.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (+.f64 (log.f64 (/.f64 D (cbrt.f64 d))) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d))))))
	60.5b	(/.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))
	47.1b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	63.9b	(exp.f64 (log.f64 (.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)))))
	60.9b	(*.f64 1/4 (exp.f64 (+.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d)) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
	57.7b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (exp.f64 (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d))))))
	25.6b	(.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))))))
	27.4b	(.f64 1/4 (.f64 (.f64 D (/.f64 D d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	60.9b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	26.0b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h (/.f64 d (*.f64 M M))))))
	63.1b	(.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)))))
	22.9b	(.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))))
	44.2b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	33.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	25.6b	(.f64 1/4 (.f64 (/.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) (cbrt.f64 d)) (.f64 (/.f64 (cbrt.f64 D) (cbrt.f64 d)) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))))
	30.5b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	60.9b	(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))))

Compiler

Compiled 9482 to 2150 computations (77.3% saved)

regimes2.9s (13.3%)

Accuracy

Total 5.1b remaining (22%)

Threshold costs 0b (0%)

Counts

183 → 3

Compiler

Compiled 72567 to 40638 computations (44% saved)

bsearch12.0ms (0.1%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	120
1	39	120
2	39	120

end439.0ms (2%)

Compiler: Compiled 1246 to 691 computations (44.5% saved)

Details

analyze2.7s (12.5%)

sample9.0s (41.6%)

simplify42.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series1.1s (5%)

rewrite125.0ms (0.6%)

simplify360.0ms (1.7%)

prune680.0ms (3.1%)

localize10.0ms (0%)

series348.0ms (1.6%)

rewrite51.0ms (0.2%)

simplify178.0ms (0.8%)

prune436.0ms (2%)

localize11.0ms (0%)

series386.0ms (1.8%)

rewrite35.0ms (0.2%)

simplify174.0ms (0.8%)

prune301.0ms (1.4%)

localize13.0ms (0.1%)

series1.7s (7.6%)

rewrite60.0ms (0.3%)

simplify152.0ms (0.7%)

prune502.0ms (2.3%)

regimes2.9s (13.3%)

bsearch12.0ms (0.1%)

simplify4.0ms (0%)

end439.0ms (2%)

Profiling