Details

analyze2.5s (13.3%)

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)

sample270.0ms (1.4%)

Algorithm

1×

intervals

Results

50.0ms	82×	body	4096	valid
37.0ms	321×	body	128	nan
29.0ms	38×	body	8192	valid
19.0ms	112×	body	128	invalid
16.0ms	33×	body	2048	valid
8.0ms	83×	body	128	valid
5.0ms	14×	body	1024	valid
1.0ms	4×	body	512	valid
0.0ms	1×	body	2048	invalid
0.0ms	2×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify44.0ms (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

59.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.2b	(.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)))))
▶	59.1b	(.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

61.2b

(*.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)))))

▶

59.1b

(*.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)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.9b	(.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)))))
✓	12.0b	(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)))
✓	17.1b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	31.8b	(+.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))))

series1.2s (6.4%)

Counts

4 → 276

Calls

4 calls:

464.0ms	(.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)))))
282.0ms	(+.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))))
263.0ms	(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)))
184.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite139.0ms (0.7%)

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)))))
35.0ms	(+.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))))
26.0ms	(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)))

simplify299.0ms (1.6%)

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

prune565.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	423	9	432
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	425	9	434

Error

32.2b

Counts

434 → 9

Alt Table

Status	Error	Program
	59.7b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	49.9b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	59.1b	(.f64 (.f64 (/.f64 c0 (.f64 2 w)) (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))))))
	61.1b	(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))))
	58.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
▶	38.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	62.7b	(.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)))))
	44.2b	(.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))))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.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 30531 to 7899 computations (74.1% saved)

localize9.0ms (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)))
✓	5.3b	(*.f64 (pow.f64 M 2) h)
✓	16.9b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
✓	16.9b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

series314.0ms (1.7%)

Counts

4 → 72

Calls

4 calls:

158.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
116.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
31.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite51.0ms (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:

10.0ms	(.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))
5.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
4.0ms	(*.f64 (pow.f64 M 2) h)

simplify144.0ms (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

prune360.0ms (1.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	214	17	231
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	218	22	240

Error

22.6b

Counts

240 → 22

Alt Table

Status	Error	Program
	57.7b	(.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))))
	58.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	58.5b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	59.7b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	58.6b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
▶	35.0b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	37.5b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	59.1b	(.f64 (.f64 (/.f64 c0 (.f64 2 w)) (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))))))
	57.7b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 (pow.f64 M 2) h))) (*.f64 (log.f64 d) 2))))
	36.5b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	36.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M 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)))
	60.2b	(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))))
	36.5b	(.f64 1/4 (.f64 (/.f64 (pow.f64 D 2) (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) 2)) (/.f64 (.f64 (pow.f64 M 2) h) (pow.f64 (cbrt.f64 d) 2))))
	60.5b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.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)))))
	49.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (sqrt.f64 M) 2) (.f64 h M))) (pow.f64 d 2)))
	58.2b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	58.2b	(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)))))
	62.7b	(.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)))))
	35.5b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	56.3b	(.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)))
	54.6b	(.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)))

Compiler

Compiled 6376 to 3974 computations (37.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.3b	(.f64 h (.f64 M M))
✓	9.4b	(/.f64 (.f64 h (.f64 M M)) d)
✓	10.6b	(/.f64 (*.f64 D D) d)
✓	12.3b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series164.0ms (0.9%)

Counts

4 → 132

Calls

4 calls:

120.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
25.0ms	(/.f64 (.f64 h (.f64 M M)) d)
11.0ms	(/.f64 (*.f64 D D) d)
8.0ms	(.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 (.f64 h (.f64 M M)) d)
4.0ms	(.f64 h (.f64 M M))
3.0ms	(/.f64 (*.f64 D D) d)

simplify129.0ms (0.7%)

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

prune268.0ms (1.4%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	146	14	160
Fresh	8	13	21
Picked	1	0	1
Done	0	0	0
Total	155	27	182

Error

20.5b

Counts

182 → 27

Alt Table

Status	Error	Program
	33.4b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	48.3b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	36.6b	(.f64 1/4 (exp.f64 (log.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))))
	58.2b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	54.1b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d)) (-.f64 (log.f64 (.f64 h (.f64 M M))) (log.f64 d)))))
	60.2b	(.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)))))
	58.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	58.2b	(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)))))
	57.7b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d)) (log.f64 (/.f64 (.f64 h (*.f64 M M)) d)))))
	58.5b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	59.7b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	33.4b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	55.9b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (/.f64 (.f64 h (.f64 M M)) d)))
	35.0b	(.f64 1/4 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 D D) d)) (cbrt.f64 (/.f64 (.f64 D D) d))) (.f64 (cbrt.f64 (/.f64 (.f64 D D) d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	54.6b	(.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)))
	36.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	49.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) 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)))
	31.4b	(.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)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.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)))))
▶	31.2b	(.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))))
	62.7b	(.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)))))
	49.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D (/.f64 D (sqrt.f64 d))) (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	58.6b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	59.1b	(.f64 (.f64 (/.f64 c0 (.f64 2 w)) (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))))))
	56.3b	(.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)))
	33.5b	(.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))))

Compiler

Compiled 5197 to 1825 computations (64.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.9b	(.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))
✓	5.1b	(.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 h (.f64 M M))
	9.4b	(/.f64 (.f64 h (.f64 M M)) d)

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))
200.0ms	(.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))

rewrite55.0ms (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:

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

simplify159.0ms (0.8%)

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

prune565.0ms (3%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	256	10	266
Fresh	5	21	26
Picked	1	0	1
Done	0	0	0
Total	262	31	293

Error

19.1b

Counts

293 → 31

Alt Table

Status	Error	Program
	33.4b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	36.6b	(.f64 1/4 (exp.f64 (log.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))))
	31.2b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (.f64 (/.f64 D (cbrt.f64 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)))))
	31.2b	(.f64 1/4 (.f64 (.f64 (cbrt.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (cbrt.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))))) (.f64 (cbrt.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d)))))
	58.2b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	39.7b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (exp.f64 (log.f64 (.f64 h (.f64 M M)))) d))))
	54.1b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (log.f64 (.f64 D D)) (log.f64 d)) (-.f64 (log.f64 (.f64 h (.f64 M M))) (log.f64 d)))))
	60.2b	(.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)))))
	58.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	58.2b	(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)))))
	29.2b	(.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))))
	57.7b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d)) (log.f64 (/.f64 (.f64 h (*.f64 M M)) d)))))
	34.5b	(.f64 1/4 (/.f64 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 D (.f64 h (.f64 M M)))) (*.f64 (cbrt.f64 d) d)))
	50.1b	(.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))))))
	62.7b	(.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)))))
	58.5b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	59.7b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	58.6b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	31.8b	(.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))) d)))
	32.3b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (/.f64 (.f64 (*.f64 M M) h) d))) d))
	35.0b	(.f64 1/4 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 D D) d)) (cbrt.f64 (/.f64 (.f64 D D) d))) (.f64 (cbrt.f64 (/.f64 (.f64 D D) d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	33.4b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	28.5b	(.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)))))
	36.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M 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)))
	31.4b	(.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)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.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)))))
	49.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D (/.f64 D (sqrt.f64 d))) (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d)))
	59.1b	(.f64 (.f64 (/.f64 c0 (.f64 2 w)) (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))))))
	56.3b	(.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)))
	28.9b	(.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))))

Compiler

Compiled 9388 to 2097 computations (77.7% saved)

regimes2.2s (11.7%)

Accuracy

Total 6.7b remaining (27.8%)

Threshold costs 0b (0%)

Counts

146 → 3

Compiler

Compiled 66607 to 34436 computations (48.3% saved)

bsearch308.0ms (1.6%)

Steps

Iters	Range		Point
9	4.616924322326168e+149	3.4156522173108783e+155	1.3559963451736178e+154
7	-3.52152986907621e+117	-4.608108930671353e+115	-3.660832784072471e+116

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	110
1	55	110
2	55	110

end4.0ms (0%)

Compiler: Compiled 77 to 46 computations (40.3% saved)

sample7.4s (39.4%)

Algorithm

1×

intervals

Results

1.6s	2145×	body	4096	valid
1.3s	12173×	body	128	nan
1.0s	1186×	body	8192	valid
665.0ms	1279×	body	2048	valid
434.0ms	4028×	body	128	invalid
345.0ms	600×	body	1024	valid
260.0ms	2360×	body	128	valid
80.0ms	276×	body	512	valid
32.0ms	154×	body	256	valid
25.0ms	52×	body	2048	invalid
22.0ms	54×	body	1024	invalid
15.0ms	45×	body	512	invalid
14.0ms	11×	body	4096	invalid
7.0ms	10×	body	8192	exit
4.0ms	22×	body	256	invalid

Compiler

Compiled 1126 to 645 computations (42.7% saved)

Details

analyze2.5s (13.3%)

sample270.0ms (1.4%)

simplify44.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0.1%)

series1.2s (6.4%)

rewrite139.0ms (0.7%)

simplify299.0ms (1.6%)

prune565.0ms (3%)

localize9.0ms (0%)

series314.0ms (1.7%)

rewrite51.0ms (0.3%)

simplify144.0ms (0.8%)

prune360.0ms (1.9%)

localize12.0ms (0.1%)

series164.0ms (0.9%)

rewrite35.0ms (0.2%)

simplify129.0ms (0.7%)

prune268.0ms (1.4%)

localize13.0ms (0.1%)

series1.6s (8.3%)

rewrite55.0ms (0.3%)

simplify159.0ms (0.8%)

prune565.0ms (3%)

regimes2.2s (11.7%)

bsearch308.0ms (1.6%)

simplify3.0ms (0%)

end4.0ms (0%)

sample7.4s (39.4%)

Profiling