Details

analyze2.6s (13.5%)

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)

sample296.0ms (1.5%)

Algorithm

1×

intervals

Results

45.0ms	394×	body	128	nan
39.0ms	63×	body	4096	valid
27.0ms	31×	body	8192	valid
23.0ms	45×	body	2048	valid
12.0ms	74×	body	128	valid
12.0ms	118×	body	128	invalid
10.0ms	26×	body	1024	valid
7.0ms	7×	body	256	valid
3.0ms	10×	body	512	valid
1.0ms	3×	body	1024	invalid
1.0ms	2×	body	2048	invalid
1.0ms	1×	body	8192	exit
0.0ms	1×	body	512	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

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

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

57.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.0b	(.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)))))
▶	58.0b	(.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)))))

Status

Error

Program

61.0b

(*.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)))))

▶

58.0b

(*.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)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.0b	(.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)))))
✓	13.1b	(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)))
✓	19.5b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	29.9b	(+.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))))

series1.4s (7.1%)

Counts

4 → 276

Calls

4 calls:

533.0ms	(.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)))))
305.0ms	(+.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))))
299.0ms	(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)))
218.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite178.0ms (0.9%)

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:

67.0ms	(+.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))))
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)))))
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)))

simplify358.0ms (1.9%)

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

prune606.0ms (3.1%)

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

28.4b

Counts

434 → 10

Alt Table

Status	Error	Program
▶	35.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	61.7b	(.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)))))
	50.2b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	58.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	58.6b	(.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)))))))
	41.5b	(.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)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 (.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))
	60.2b	(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))))
	59.1b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))

Compiler

Compiled 30571 to 7931 computations (74.1% 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)))
✓	7.8b	(*.f64 (pow.f64 M 2) h)
✓	12.6b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	16.9b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series339.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

155.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
137.0ms	(/.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))
10.0ms	(*.f64 (pow.f64 M 2) h)

rewrite56.0ms (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)))
9.0ms	(/.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)

simplify160.0ms (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

prune418.0ms (2.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	215	16	231
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	220	21	241

Error

19.6b

Counts

241 → 21

Alt Table

Status	Error	Program
	52.9b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	57.9b	(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)))))
▶	30.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	54.8b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	35.7b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	33.0b	(.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)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	58.6b	(.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)))))))
	53.0b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) (pow.f64 d 2)))
	31.1b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	46.8b	(*.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)))))
	50.8b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	47.4b	(.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)))
	32.2b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	54.8b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	61.0b	(.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)))))
	32.6b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	59.1b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	57.5b	(.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))))
	32.9b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) 2)) (pow.f64 (cbrt.f64 d) 2)))

Compiler

Compiled 6308 to 3908 computations (38% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.3b	(/.f64 (.f64 h (.f64 M M)) d)
✓	7.0b	(/.f64 (*.f64 D D) d)
✓	7.8b	(.f64 h (.f64 M M))
✓	11.6b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series185.0ms (1%)

Counts

4 → 132

Calls

4 calls:

128.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
32.0ms	(/.f64 (.f64 h (.f64 M M)) d)
13.0ms	(.f64 h (.f64 M M))
11.0ms	(/.f64 (*.f64 D D) d)

rewrite38.0ms (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:

12.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
5.0ms	(/.f64 (.f64 h (.f64 M M)) d)
4.0ms	(.f64 h (.f64 M M))
4.0ms	(/.f64 (*.f64 D D) d)

simplify145.0ms (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

prune281.0ms (1.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	146	14	160
Fresh	6	14	20
Picked	1	0	1
Done	0	0	0
Total	153	28	181

Error

16.1b

Counts

181 → 28

Alt Table

Status	Error	Program
	57.9b	(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)))))
	45.4b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	54.8b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
▶	25.3b	(.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))))
	54.8b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	47.2b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	40.4b	(.f64 1/4 (.f64 (exp.f64 (log.f64 (/.f64 (.f64 D D) d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	32.6b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	33.0b	(.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)) (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 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	59.1b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	43.9b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) d)))
	58.6b	(.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)))))))
	30.6b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 h (/.f64 (*.f64 M M) d))))
	57.4b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d)) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
	31.1b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	46.8b	(*.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)))))
	57.6b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d)) (-.f64 (+.f64 (log.f64 h) (log.f64 (.f64 M M))) (log.f64 d)))))
	50.8b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	32.0b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (expm1.f64 (log1p.f64 (/.f64 (.f64 h (*.f64 M M)) d)))))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	57.5b	(.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))))
	27.9b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d D)) (/.f64 (.f64 h (.f64 M M)) d)))
	31.8b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (.f64 M M) (cbrt.f64 d))))
	25.9b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	61.0b	(.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)))))
	45.0b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (exp.f64 (+.f64 (log.f64 h) (log.f64 (.f64 M M)))) d)))

Compiler

Compiled 5183 to 1835 computations (64.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.7b	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
✓	5.3b	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))
	6.3b	(/.f64 (.f64 h (.f64 M M)) d)
	7.8b	(.f64 h (.f64 M M))

series1.6s (8.3%)

Counts

2 → 96

Calls

2 calls:

1.4s	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))
178.0ms	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))

rewrite67.0ms (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 (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))
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)))

simplify168.0ms (0.9%)

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

prune559.0ms (2.9%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	256	10	266
Fresh	9	18	27
Picked	1	0	1
Done	0	0	0
Total	266	28	294

Error

14.5b

Counts

294 → 28

Alt Table

Status	Error	Program
	24.8b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (.f64 h (*.f64 M M))) (/.f64 1 d))))
	57.9b	(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)))))
	41.9b	(.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))))
	24.9b	(.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))))
	54.8b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	22.0b	(.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))))
	25.9b	(.f64 1/4 (.f64 D (/.f64 (.f64 D (/.f64 (.f64 (*.f64 M M) h) d)) d)))
	61.0b	(.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)))))
	24.1b	(.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)))))
	26.7b	(.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))
	47.2b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	25.3b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (*.f64 M M) (cbrt.f64 d)))))
	40.4b	(.f64 1/4 (.f64 (exp.f64 (log.f64 (/.f64 (.f64 D D) d))) (/.f64 (.f64 h (*.f64 M M)) d)))
	33.0b	(.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)) (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 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	59.1b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	27.5b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (/.f64 (.f64 (*.f64 M M) h) d))) d))
	58.6b	(.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)))))))
	30.6b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 h (/.f64 (*.f64 M M) d))))
	57.4b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d)) (-.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M))) (log.f64 d)))))
	46.8b	(*.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)))))
	48.7b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (exp.f64 (+.f64 (log.f64 (/.f64 D (cbrt.f64 d))) (log.f64 (/.f64 (.f64 h (*.f64 M M)) d))))))
	50.8b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	57.5b	(.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))))
	27.9b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d D)) (/.f64 (.f64 h (.f64 M M)) d)))
	25.9b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))

Compiler

Compiled 9258 to 2033 computations (78% saved)

regimes2.0s (10.5%)

Accuracy

Total 6.9b remaining (28.2%)

Threshold costs 0b (0%)

Counts

122 → 3

Compiler

Compiled 38234 to 24700 computations (35.4% saved)

bsearch312.0ms (1.6%)

Steps

Iters	Range		Point
8	2.0398302160041486e+73	5.4522540986684987e+76	2.071342702714757e+76
7	-1.6853368466510034e+176	-3.5653889882806348e+174	-3.6081226175982936e+174

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	82
1	42	82
2	42	82

end1.0ms (0%)

Compiler: Compiled 59 to 32 computations (45.8% saved)

sample7.4s (38.6%)

Algorithm

1×

intervals

Results

1.6s	2118×	body	4096	valid
1.3s	12116×	body	128	nan
974.0ms	1157×	body	8192	valid
681.0ms	1291×	body	2048	valid
447.0ms	4200×	body	128	invalid
266.0ms	640×	body	1024	valid
251.0ms	2371×	body	128	valid
123.0ms	273×	body	512	valid
30.0ms	150×	body	256	valid
30.0ms	59×	body	2048	invalid
20.0ms	51×	body	1024	invalid
12.0ms	41×	body	512	invalid
8.0ms	13×	body	4096	invalid
4.0ms	21×	body	256	invalid
4.0ms	5×	body	8192	exit

Compiler

Compiled 978 to 568 computations (41.9% saved)

Details

analyze2.6s (13.5%)

sample296.0ms (1.5%)

simplify43.0ms (0.2%)

prune7.0ms (0%)

localize18.0ms (0.1%)

series1.4s (7.1%)

rewrite178.0ms (0.9%)

simplify358.0ms (1.9%)

prune606.0ms (3.1%)

localize10.0ms (0.1%)

series339.0ms (1.8%)

rewrite56.0ms (0.3%)

simplify160.0ms (0.8%)

prune418.0ms (2.2%)

localize11.0ms (0.1%)

series185.0ms (1%)

rewrite38.0ms (0.2%)

simplify145.0ms (0.8%)

prune281.0ms (1.5%)

localize15.0ms (0.1%)

series1.6s (8.3%)

rewrite67.0ms (0.3%)

simplify168.0ms (0.9%)

prune559.0ms (2.9%)

regimes2.0s (10.5%)

bsearch312.0ms (1.6%)

simplify4.0ms (0%)

end1.0ms (0%)

sample7.4s (38.6%)

Profiling