Details

analyze2.6s (16%)

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)

sample8.9s (54%)

Results

3.1s	16467×	body	128	invalid
2.1s	2152×	body	4096	valid
1.4s	1193×	body	8192	valid
1.1s	1393×	body	2048	valid
464.0ms	2421×	body	128	valid
390.0ms	618×	body	1024	valid
147.0ms	315×	body	512	valid
55.0ms	164×	body	256	valid
43.0ms	53×	body	2048	invalid
35.0ms	58×	body	1024	invalid
17.0ms	38×	body	512	invalid
17.0ms	18×	body	4096	invalid
10.0ms	31×	body	256	invalid
4.0ms	4×	body	8192	exit

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
416×	`fma-def_binary64`
302×	`associate-/l*_binary64`
217×	`fma-neg_binary64`
189×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	78
1	64	74
2	314	74
3	3572	67
4	4695	67

Stop Event

1×	node limit

Counts

1 → 2

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

60.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.9b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 (/.f64 (/.f64 c0 (.f64 D D)) h) w) (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)))))
▶	60.5b	(.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)))))

Status

Error

Program

62.9b

(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 (/.f64 (/.f64 c0 (*.f64 D D)) h) w) (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)))))

▶

60.5b

(*.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)))))

Compiler

Compiled 321 to 134 computations (58.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.7b	(.f64 (.f64 w h) (*.f64 D D))
✓	11.0b	(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)))
✓	15.6b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	34.4b	(+.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))))

series552.0ms (3.3%)

Counts

4 → 240

Calls

4 calls:

204.0ms	(+.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))))
185.0ms	(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)))
145.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
16.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite54.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
194×	`add-cbrt-cube_binary64`
191×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	110
1	407	108

Stop Event

1×	node limit

Counts

4 → 128

Calls

4 calls:

50.0ms	(.f64 (.f64 w h) (*.f64 D D))
50.0ms	(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)))
50.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
50.0ms	(+.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))))

simplify163.0ms (1%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-def_binary64`
505×	`unswap-sqr_binary64`
294×	`associate-r_binary64`
256×	`times-frac_binary64`
255×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	11169
1	777	11085
2	3538	11033

Stop Event

1×	node limit

Counts

368 → 211

prune376.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	360	7	367
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	362	7	369

Error

27.9b

Counts

369 → 7

Alt Table

Status	Error	Program
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (hypot.f64 (/.f64 (.f64 d (sqrt.f64 c0)) (.f64 D (sqrt.f64 (.f64 w h)))) (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 w) (/.f64 (.f64 d d) (.f64 h (.f64 D D)))) 2) (.f64 M M)) 1/4)) 2))
	49.0b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) w) (/.f64 d (.f64 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)))))
▶	39.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (/.f64 (.f64 (*.f64 M M) w) (/.f64 c0 h)) 1/2)))
	42.9b	(.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))))
	55.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))

Compiler

Compiled 21455 to 6251 computations (70.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.1b	(.f64 (.f64 M M) w)
✓	10.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (/.f64 (.f64 (*.f64 M M) w) (/.f64 c0 h)) 1/2)))
✓	13.2b	(/.f64 (.f64 (.f64 M M) w) (/.f64 c0 h))
✓	16.6b	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (/.f64 (.f64 (*.f64 M M) w) (/.f64 c0 h)) 1/2))

series569.0ms (3.4%)

Counts

4 → 216

Calls

4 calls:

299.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (/.f64 (.f64 (*.f64 M M) w) (/.f64 c0 h)) 1/2))
222.0ms	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (/.f64 (.f64 (*.f64 M M) w) (/.f64 c0 h)) 1/2)))
41.0ms	(/.f64 (.f64 (.f64 M M) w) (/.f64 c0 h))
8.0ms	(.f64 (.f64 M M) w)

rewrite44.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

220×	`add-sqr-sqrt_binary64`
205×	`add-log-exp_binary64`
205×	`log1p-expm1-u_binary64`
205×	`expm1-log1p-u_binary64`
204×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	79
1	440	79

Stop Event

1×	node limit

Counts

4 → 95

Calls

4 calls:

42.0ms	(.f64 (.f64 M M) w)
42.0ms	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (/.f64 (.f64 (*.f64 M M) w) (/.f64 c0 h)) 1/2)))
42.0ms	(/.f64 (.f64 (.f64 M M) w) (/.f64 c0 h))
42.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (/.f64 (.f64 (*.f64 M M) w) (/.f64 c0 h)) 1/2))

simplify189.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

960×	`associate-/r/_binary64`
831×	`associate-/l/_binary64`
527×	`unswap-sqr_binary64`
390×	`times-frac_binary64`
259×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	4392
1	92	4392
2	314	4392
3	2387	4392
4	2464	4392
5	2612	4392
6	2944	4392
7	3621	4392
8	3716	4392

Stop Event

1×	node limit

Counts

311 → 106

prune137.0ms (0.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	99	14	113

Error

14.0b

Counts

113 → 14

Alt Table

Status	Error	Program
	38.4b	(.f64 (/.f64 c0 (.f64 2 w)) (/.f64 (.f64 (.f64 D (/.f64 D d)) (.f64 (.f64 (.f64 M M) w) 1/2)) (.f64 d (/.f64 c0 h))))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	32.0b	(log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (/.f64 (.f64 M M) (/.f64 (/.f64 c0 h) w))) (pow.f64 (/.f64 D d) 2)) (.f64 1/2 (/.f64 c0 w))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (hypot.f64 (/.f64 (.f64 d (sqrt.f64 c0)) (.f64 D (sqrt.f64 (.f64 w h)))) (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 w) (/.f64 (.f64 d d) (.f64 h (.f64 D D)))) 2) (.f64 M M)) 1/4)) 2))
	48.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (.f64 (/.f64 (.f64 M (sqrt.f64 w)) c0) (/.f64 (.f64 M (sqrt.f64 w)) (/.f64 1 h))) 1/2)))
	37.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 h (pow.f64 M 2))) (pow.f64 d 2)))
	36.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (.f64 (/.f64 M 1) (/.f64 (*.f64 M w) (/.f64 c0 h))) 1/2)))
	34.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (.f64 (/.f64 (.f64 (/.f64 M d) (.f64 M h)) d) w) (/.f64 (.f64 D D) c0))))
▶	27.8b	(.f64 (/.f64 (.f64 D (.f64 D 1/4)) d) (.f64 (/.f64 M d) (*.f64 M h)))
	40.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (.f64 (.f64 (/.f64 h c0) (.f64 M M)) w) 1/2)))
	38.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (/.f64 (.f64 w (*.f64 h (pow.f64 M 2))) c0) 1/2)))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) w) (/.f64 d (.f64 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)))))
	63.4b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (.f64 (/.f64 D d) (.f64 (sqrt.f64 1/2) (/.f64 M (sqrt.f64 (/.f64 (/.f64 c0 h) w))))) 2))
	55.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))

Compiler

Compiled 3837 to 1772 computations (53.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.1b	(.f64 (/.f64 M d) (.f64 M h))
✓	8.4b	(/.f64 (.f64 D (.f64 D 1/4)) d)
✓	11.7b	(.f64 (/.f64 (.f64 D (.f64 D 1/4)) d) (.f64 (/.f64 M d) (*.f64 M h)))

series256.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

188.0ms	(.f64 (/.f64 (.f64 D (.f64 D 1/4)) d) (.f64 (/.f64 M d) (*.f64 M h)))
45.0ms	(/.f64 (.f64 D (.f64 D 1/4)) d)
23.0ms	(.f64 (/.f64 M d) (.f64 M h))

rewrite66.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
162×	`associate-r_binary64`
138×	`add-sqr-sqrt_binary64`
129×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	279	42
2	3970	42

Stop Event

1×	node limit

Counts

3 → 109

Calls

3 calls:

62.0ms	(.f64 (/.f64 M d) (.f64 M h))
62.0ms	(/.f64 (.f64 D (.f64 D 1/4)) d)
62.0ms	(.f64 (/.f64 (.f64 D (.f64 D 1/4)) d) (.f64 (/.f64 M d) (*.f64 M h)))

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

744×	`associate-/l*_binary64`
541×	`associate-l_binary64`
532×	`associate-r_binary64`
399×	`associate-/r*_binary64`
271×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	1656
1	55	1656
2	146	1656
3	736	1656

Stop Event

1×	node limit

Counts

217 → 117

prune216.0ms (1.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	104	13	117
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	110	21	131

Error

9.8b

Counts

131 → 21

Alt Table

Status	Error	Program
▶	21.9b	(/.f64 (.f64 D (.f64 M (.f64 h (/.f64 M d)))) (.f64 4 (/.f64 d D)))
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	32.0b	(log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (/.f64 (.f64 M M) (/.f64 (/.f64 c0 h) w))) (pow.f64 (/.f64 D d) 2)) (.f64 1/2 (/.f64 c0 w))))
	46.5b	(/.f64 (/.f64 (.f64 (.f64 (.f64 D (.f64 D 1/4)) (*.f64 M h)) (/.f64 M d)) (sqrt.f64 d)) (sqrt.f64 d))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (hypot.f64 (/.f64 (.f64 d (sqrt.f64 c0)) (.f64 D (sqrt.f64 (.f64 w h)))) (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 w) (/.f64 (.f64 d d) (.f64 h (.f64 D D)))) 2) (.f64 M M)) 1/4)) 2))
	34.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (.f64 (/.f64 (.f64 (/.f64 M d) (.f64 M h)) d) w) (/.f64 (.f64 D D) c0))))
	28.6b	(cbrt.f64 (pow.f64 (.f64 (.f64 M h) (.f64 (/.f64 D (.f64 4 (/.f64 d D))) (/.f64 M d))) 3))
	27.8b	(.f64 (/.f64 (.f64 D (.f64 D 1/4)) d) (/.f64 M (/.f64 d (.f64 M h))))
	23.6b	(.f64 (.f64 (/.f64 D (pow.f64 (cbrt.f64 d) 2)) (/.f64 (.f64 D 1/4) (cbrt.f64 d))) (.f64 (/.f64 M d) (*.f64 M h)))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) w) (/.f64 d (.f64 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)))))
	63.4b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (.f64 (/.f64 D d) (.f64 (sqrt.f64 1/2) (/.f64 M (sqrt.f64 (/.f64 (/.f64 c0 h) w))))) 2))
	26.9b	(/.f64 (.f64 (.f64 M (.f64 M h)) (/.f64 D (.f64 4 (/.f64 d D)))) d)
	28.1b	(/.f64 (/.f64 (.f64 (.f64 (.f64 D (.f64 D 1/4)) (*.f64 M h)) (/.f64 M d)) (pow.f64 (cbrt.f64 d) 2)) (cbrt.f64 d))
	48.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (.f64 (/.f64 (.f64 M (sqrt.f64 w)) c0) (/.f64 (.f64 M (sqrt.f64 w)) (/.f64 1 h))) 1/2)))
	28.8b	(/.f64 (.f64 D (.f64 M (.f64 M h))) (.f64 (*.f64 4 (/.f64 d D)) d))
	43.7b	(.f64 (pow.f64 (/.f64 (.f64 D 1/2) (sqrt.f64 d)) 2) (.f64 (/.f64 M d) (.f64 M h)))
	26.6b	(.f64 (expm1.f64 (log1p.f64 (/.f64 D (.f64 4 (/.f64 d D))))) (.f64 (/.f64 M d) (.f64 M h)))
	27.0b	(/.f64 (.f64 D (.f64 D 1/4)) (/.f64 d (.f64 M (.f64 h (/.f64 M d)))))
	22.5b	(pow.f64 (.f64 (.f64 M h) (.f64 (/.f64 D (.f64 4 (/.f64 d D))) (/.f64 M d))) 1)
	45.7b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 D (.f64 D 1/4))) 2) (sqrt.f64 d)) (/.f64 (cbrt.f64 (.f64 D (.f64 D 1/4))) (sqrt.f64 d))) (.f64 (/.f64 M d) (.f64 M h)))
	55.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))

Compiler

Compiled 3307 to 1669 computations (49.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(.f64 M (.f64 h (/.f64 M d)))
✓	4.8b	(/.f64 (.f64 D (.f64 M (.f64 h (/.f64 M d)))) (.f64 4 (/.f64 d D)))
✓	5.3b	(*.f64 h (/.f64 M d))
✓	6.0b	(.f64 D (.f64 M (*.f64 h (/.f64 M d))))

series199.0ms (1.2%)

Counts

4 → 168

Calls

4 calls:

109.0ms	(/.f64 (.f64 D (.f64 M (.f64 h (/.f64 M d)))) (.f64 4 (/.f64 d D)))
39.0ms	(.f64 M (.f64 h (/.f64 M d)))
38.0ms	(.f64 D (.f64 M (*.f64 h (/.f64 M d))))
12.0ms	(*.f64 h (/.f64 M d))

rewrite68.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

267×	`log1p-udef_binary64`
149×	`times-frac_binary64`
146×	`add-sqr-sqrt_binary64`
145×	`associate-r_binary64`
137×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	290	52
2	4456	52

Stop Event

1×	node limit

Counts

4 → 124

Calls

4 calls:

65.0ms	(.f64 M (.f64 h (/.f64 M d)))
65.0ms	(/.f64 (.f64 D (.f64 M (.f64 h (/.f64 M d)))) (.f64 4 (/.f64 d D)))
65.0ms	(*.f64 h (/.f64 M d))
65.0ms	(.f64 D (.f64 M (*.f64 h (/.f64 M d))))

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

770×	`associate-/l*_binary64`
609×	`associate-l_binary64`
564×	`associate-r_binary64`
436×	`associate-/r*_binary64`
302×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	2292
1	70	2292
2	169	2292
3	784	2292

Stop Event

1×	node limit

Counts

292 → 135

prune261.0ms (1.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	124	11	135
Fresh	12	8	20
Picked	1	0	1
Done	0	0	0
Total	137	19	156

Error

6.8b

Counts

156 → 19

Alt Table

Status	Error	Program
	32.0b	(log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (/.f64 (.f64 M M) (/.f64 (/.f64 c0 h) w))) (pow.f64 (/.f64 D d) 2)) (.f64 1/2 (/.f64 c0 w))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (hypot.f64 (/.f64 (.f64 d (sqrt.f64 c0)) (.f64 D (sqrt.f64 (.f64 w h)))) (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 w) (/.f64 (.f64 d d) (.f64 h (.f64 D D)))) 2) (.f64 M M)) 1/4)) 2))
	20.7b	(.f64 (/.f64 (.f64 (.f64 h (/.f64 M d)) (.f64 D M)) (*.f64 d 4)) D)
	33.3b	(/.f64 (.f64 D (.f64 M (exp.f64 (log.f64 (.f64 h (/.f64 M d)))))) (.f64 4 (/.f64 d D)))
	28.1b	(/.f64 (/.f64 (.f64 (.f64 (.f64 D (.f64 D 1/4)) (*.f64 M h)) (/.f64 M d)) (pow.f64 (cbrt.f64 d) 2)) (cbrt.f64 d))
	32.2b	(/.f64 (.f64 D (.f64 M (-.f64 (exp.f64 (log1p.f64 (.f64 h (/.f64 M d)))) 1))) (.f64 4 (/.f64 d D)))
	28.8b	(/.f64 (.f64 D (.f64 M (.f64 M h))) (.f64 (*.f64 4 (/.f64 d D)) d))
	23.8b	(/.f64 (/.f64 (.f64 (.f64 D M) (.f64 M h)) d) (.f64 4 (/.f64 d D)))
	27.0b	(/.f64 (.f64 D (.f64 D 1/4)) (/.f64 d (.f64 M (.f64 h (/.f64 M d)))))
	29.8b	(/.f64 (/.f64 (.f64 D (.f64 (pow.f64 M 2) h)) d) (*.f64 4 (/.f64 d D)))
	55.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	18.4b	(pow.f64 (/.f64 (/.f64 (/.f64 (/.f64 4 (/.f64 D d)) M) (*.f64 h (/.f64 M d))) D) -1)
	59.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	21.2b	(.f64 (/.f64 D d) (.f64 (.f64 (.f64 h (/.f64 M d)) (*.f64 D M)) 1/4))
	23.6b	(/.f64 (expm1.f64 (log1p.f64 (.f64 (.f64 h (/.f64 M d)) (.f64 D M)))) (.f64 4 (/.f64 d D)))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) w) (/.f64 d (.f64 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)))))
	18.4b	(.f64 (.f64 D 1/4) (/.f64 (*.f64 h (/.f64 M d)) (/.f64 (/.f64 d D) M)))
	20.8b	(.f64 (/.f64 (.f64 D M) (/.f64 d D)) (/.f64 (*.f64 h (/.f64 M d)) 4))
	21.3b	(.f64 1/4 (/.f64 (.f64 (.f64 h (/.f64 M d)) (.f64 D M)) (/.f64 d D)))

Compiler

Compiled 3073 to 1261 computations (59% saved)

regimes1.3s (8%)

Accuracy

Total 10.0b remaining (50.2%)

Threshold costs 0b (0%)

Counts

113 → 4

Compiler

Compiled 30140 to 19911 computations (33.9% saved)

bsearch5.0ms (0%)

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

simplify10.0ms (0.1%)

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	49	402
1	69	402
2	77	402
3	81	402
4	83	402

Stop Event

1×

saturated

end268.0ms (1.6%)

Compiler: Compiled 1048 to 455 computations (56.6% saved)

Details

analyze2.6s (16%)

sample8.9s (54%)

simplify31.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series552.0ms (3.3%)

rewrite54.0ms (0.3%)

simplify163.0ms (1%)

prune376.0ms (2.3%)

localize18.0ms (0.1%)

series569.0ms (3.4%)

rewrite44.0ms (0.3%)

simplify189.0ms (1.1%)

prune137.0ms (0.8%)

localize9.0ms (0.1%)

series256.0ms (1.5%)

rewrite66.0ms (0.4%)

simplify41.0ms (0.3%)

prune216.0ms (1.3%)

localize9.0ms (0.1%)

series199.0ms (1.2%)

rewrite68.0ms (0.4%)

simplify76.0ms (0.5%)

prune261.0ms (1.6%)

regimes1.3s (8%)

bsearch5.0ms (0%)

simplify10.0ms (0.1%)

end268.0ms (1.6%)

Profiling