Details

analyze2.6s (14.8%)

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)

sample304.0ms (1.7%)

Algorithm

1×

intervals

Results

52.0ms	48×	body	8192	valid
37.0ms	370×	body	128	nan
32.0ms	53×	body	4096	valid
24.0ms	49×	body	2048	valid
18.0ms	145×	body	128	invalid
10.0ms	71×	body	128	valid
9.0ms	24×	body	1024	valid
2.0ms	8×	body	512	valid
1.0ms	2×	body	2048	invalid
1.0ms	3×	body	256	valid
0.0ms	2×	body	256	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify46.0ms (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

58.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.6b	(.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)))))
▶	58.7b	(.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

61.6b

(*.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)))))

▶

58.7b

(*.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
✓	12.9b	(.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)))))
✓	13.8b	(.f64 (.f64 w h) (*.f64 D D))
✓	15.0b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	31.2b	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))

series1.0s (6%)

Counts

4 → 240

Calls

4 calls:

513.0ms	(.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)))))
308.0ms	(+.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))))
201.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
25.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite129.0ms (0.7%)

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:

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)))))
40.0ms	(+.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))))
11.0ms	(.f64 (.f64 w h) (*.f64 D D))
10.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

simplify320.0ms (1.8%)

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

prune624.0ms (3.6%)

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

25.1b

Counts

465 → 11

Alt Table

Status	Error	Program
	58.5b	(/.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))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	59.7b	(.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (.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)))))))
	61.6b	(.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)))))
	59.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 (.f64 w h) D) D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	61.6b	(.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)))))
	57.0b	(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))))
▶	31.2b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	60.3b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	47.3b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	38.3b	(.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 d 2) c0))))

Compiler

Compiled 31414 to 6939 computations (77.9% saved)

localize10.0ms (0.1%)

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)))
✓	7.6b	(*.f64 (pow.f64 M 2) h)
✓	12.2b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
✓	16.0b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

series344.0ms (2%)

Counts

4 → 72

Calls

4 calls:

147.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
132.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
54.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
11.0ms	(*.f64 (pow.f64 M 2) h)

rewrite50.0ms (0.3%)

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)))
7.0ms	(/.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)

simplify157.0ms (0.9%)

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

prune422.0ms (2.4%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	218	13	231
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	221	21	242

Error

17.9b

Counts

242 → 21

Alt Table

Status	Error	Program
	58.5b	(/.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))
	30.5b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	59.0b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (.f64 (log.f64 d) 2))))
	59.7b	(.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (.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)))))))
▶	28.3b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	61.6b	(.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)))))
	28.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	57.0b	(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))))
	42.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 D (.f64 h (*.f64 M M)))) (pow.f64 d 2)))
	57.8b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	59.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 (.f64 w h) D) D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	61.6b	(.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)))))
	29.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	29.1b	(.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))))
	56.1b	(.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)))
	60.3b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	51.9b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	48.1b	(.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)))))
	28.3b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	60.8b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (.f64 (log.f64 d) 2))))

Compiler

Compiled 6446 to 3954 computations (38.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.2b	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
✓	5.6b	(.f64 D (.f64 (pow.f64 M 2) h))
	7.6b	(*.f64 (pow.f64 M 2) h)
✓	12.2b	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))

series194.0ms (1.1%)

Counts

3 → 100

Calls

3 calls:

134.0ms	(/.f64 (.f64 D (.f64 D (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2))
34.0ms	(.f64 D (.f64 D (*.f64 (pow.f64 M 2) h)))
26.0ms	(.f64 D (.f64 (pow.f64 M 2) h))

rewrite28.0ms (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:

10.0ms	(/.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))

simplify135.0ms (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 → 135

Iterations

Useful iterations: 3 (0.0ms)

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

prune355.0ms (2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	7	13	20
Picked	1	0	1
Done	0	0	0
Total	180	22	202

Error

15.7b

Counts

202 → 22

Alt Table

Status	Error	Program
	58.5b	(/.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))
	30.5b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	59.0b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (.f64 (log.f64 d) 2))))
	59.7b	(.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (.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)))))))
	61.6b	(.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)))))
	25.2b	(.f64 1/4 (/.f64 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) d) d))
	59.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 (.f64 w h) D) D)) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
	27.1b	(.f64 1/4 (/.f64 (.f64 D (.f64 (.f64 D (pow.f64 M 2)) h)) (pow.f64 d 2)))
	24.4b	(.f64 1/4 (/.f64 D (/.f64 d (.f64 (.f64 h (.f64 M M)) (/.f64 D d)))))
	61.6b	(.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)))))
	29.1b	(.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))))
	56.1b	(.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)))
	60.3b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	23.7b	(.f64 1/4 (.f64 (/.f64 D d) (/.f64 (.f64 D (.f64 (pow.f64 M 2) h)) d)))
	51.9b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
▶	23.3b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))
	57.0b	(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))))
	27.6b	(.f64 1/4 (/.f64 D (/.f64 (pow.f64 d 2) (.f64 D (*.f64 (pow.f64 M 2) h)))))
	26.0b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 M (*.f64 h M)))) (pow.f64 d 2)))
	45.4b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (.f64 M (sqrt.f64 h)) (.f64 M (sqrt.f64 h))))) (pow.f64 d 2)))
	60.8b	(*.f64 1/4 (exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (+.f64 (log.f64 D) (log.f64 M)) (log.f64 h)))))

Compiler

Compiled 5268 to 2988 computations (43.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))
✓	4.2b	(.f64 (/.f64 D d) (.f64 (.f64 h (.f64 M M)) (/.f64 D d)))
✓	7.6b	(.f64 h (.f64 M M))
✓	9.3b	(.f64 (.f64 h (*.f64 M M)) (/.f64 D d))

series341.0ms (2%)

Counts

4 → 168

Calls

4 calls:

158.0ms	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))
123.0ms	(.f64 (/.f64 D d) (.f64 (.f64 h (.f64 M M)) (/.f64 D d)))
52.0ms	(.f64 (.f64 h (*.f64 M M)) (/.f64 D d))
8.0ms	(.f64 h (.f64 M M))

rewrite67.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

176×	`add-cbrt-cube_binary64`
176×	`add-exp-log_binary64`
106×	`cbrt-unprod_binary64`
106×	`prod-exp_binary64`
52×	`pow1_binary64`

Counts

4 → 172

Calls

4 calls:

13.0ms	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))
11.0ms	(.f64 (/.f64 D d) (.f64 (.f64 h (.f64 M M)) (/.f64 D d)))
8.0ms	(.f64 (.f64 h (*.f64 M M)) (/.f64 D d))
7.0ms	(.f64 h (.f64 M M))

simplify149.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

893×	`times-frac_binary64`
477×	`associate-r_binary64`
412×	`associate-/r*_binary64`
405×	`associate-l_binary64`
298×	`associate-/r/_binary64`

Counts

340 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	7488
1	506	5994
2	2180	5886
3	5199	5886

prune383.0ms (2.2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	224	11	235
Fresh	9	12	21
Picked	1	0	1
Done	0	0	0
Total	234	23	257

Error

13.6b

Counts

257 → 23

Alt Table

Status	Error	Program
	58.5b	(/.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))
	30.5b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	59.7b	(.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (.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)))))))
	61.6b	(.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)))))
	24.0b	(/.f64 (.f64 1/4 (.f64 D (.f64 (.f64 h (*.f64 M M)) (/.f64 D d)))) d)
	21.5b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 h (.f64 (*.f64 M M) (/.f64 D d)))))
	28.6b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (sqrt.f64 (.f64 (.f64 h (.f64 M M)) (/.f64 D d))) (sqrt.f64 (.f64 (.f64 h (*.f64 M M)) (/.f64 D d))))))
	27.1b	(.f64 1/4 (/.f64 (.f64 D (.f64 (.f64 D (pow.f64 M 2)) h)) (pow.f64 d 2)))
	24.0b	(.f64 1/4 (/.f64 (.f64 D (/.f64 (.f64 D (.f64 (*.f64 M M) h)) d)) d))
	24.4b	(.f64 1/4 (/.f64 D (/.f64 d (.f64 (.f64 h (.f64 M M)) (/.f64 D d)))))
	61.6b	(.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)))))
	27.6b	(.f64 1/4 (/.f64 D (/.f64 (pow.f64 d 2) (.f64 D (*.f64 (pow.f64 M 2) h)))))
	60.3b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	27.3b	(.f64 1/4 (log.f64 (pow.f64 (exp.f64 (/.f64 (.f64 D (.f64 (.f64 M M) h)) d)) (/.f64 D d))))
	57.2b	(.f64 1/4 (.f64 (/.f64 D d) (exp.f64 (+.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 (/.f64 D d))))))
	51.9b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	26.0b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 M (*.f64 h M)))) (pow.f64 d 2)))
	56.7b	(*.f64 1/4 (exp.f64 (+.f64 (log.f64 (/.f64 D d)) (+.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 (/.f64 D d))))))
	20.2b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (.f64 (*.f64 h M) M) (/.f64 D d))))
	43.7b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) (/.f64 D d))))
	54.1b	(.f64 1/4 (.f64 (/.f64 D d) (*.f64 (exp.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M)))) (/.f64 D d))))
	23.6b	(.f64 1/4 (.f64 (/.f64 D d) (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 D (cbrt.f64 d)))))

Compiler

Compiled 6432 to 1671 computations (74% saved)

regimes2.3s (13%)

Accuracy

Total 6.8b remaining (29.4%)

Threshold costs 0b (0%)

Counts

131 → 2

Compiler

Compiled 62645 to 30589 computations (51.2% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 58 to 21 computations (63.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	136
1	60	136
2	67	136
3	71	136
4	73	136
5	73	136

end1.0ms (0%)

Compiler: Compiled 97 to 44 computations (54.6% saved)

sample7.5s (42.6%)

Algorithm

1×

intervals

Results

1.5s	2095×	body	4096	valid
1.3s	11780×	body	128	nan
1.1s	1175×	body	8192	valid
730.0ms	1293×	body	2048	valid
434.0ms	3994×	body	128	invalid
264.0ms	614×	body	1024	valid
250.0ms	2382×	body	128	valid
93.0ms	287×	body	512	valid
32.0ms	154×	body	256	valid
25.0ms	63×	body	1024	invalid
24.0ms	46×	body	2048	invalid
11.0ms	15×	body	8192	exit
8.0ms	29×	body	512	invalid
7.0ms	12×	body	4096	invalid
7.0ms	35×	body	256	invalid

Compiler

Compiled 861 to 465 computations (46% saved)

Details

analyze2.6s (14.8%)

sample304.0ms (1.7%)

simplify46.0ms (0.3%)

prune5.0ms (0%)

localize18.0ms (0.1%)

series1.0s (6%)

rewrite129.0ms (0.7%)

simplify320.0ms (1.8%)

prune624.0ms (3.6%)

localize10.0ms (0.1%)

series344.0ms (2%)

rewrite50.0ms (0.3%)

simplify157.0ms (0.9%)

prune422.0ms (2.4%)

localize10.0ms (0.1%)

series194.0ms (1.1%)

rewrite28.0ms (0.2%)

simplify135.0ms (0.8%)

prune355.0ms (2%)

localize9.0ms (0%)

series341.0ms (2%)

rewrite67.0ms (0.4%)

simplify149.0ms (0.9%)

prune383.0ms (2.2%)

regimes2.3s (13%)

bsearch10.0ms (0.1%)

simplify5.0ms (0%)

end1.0ms (0%)

sample7.5s (42.6%)

Profiling