Details

analyze2.9s (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)

sample9.1s (47%)

Results

3.1s	15874×	body	128	invalid
2.2s	2204×	body	4096	valid
1.4s	1191×	body	8192	valid
1.0s	1267×	body	2048	valid
479.0ms	2436×	body	128	valid
462.0ms	710×	body	1024	valid
139.0ms	299×	body	512	valid
48.0ms	149×	body	256	valid
43.0ms	55×	body	2048	invalid
42.0ms	56×	body	1024	invalid
20.0ms	41×	body	512	invalid
11.0ms	10×	body	8192	exit
8.0ms	9×	body	4096	invalid
7.0ms	22×	body	256	invalid

Compiler

Compiled 176 to 65 computations (63.1% 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

prune6.0ms (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

59.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.3b	(.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)))))
▶	60.1b	(.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

62.3b

(*.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)))))

▶

60.1b

(*.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)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.8b	(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)))
✓	14.2b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
✓	17.0b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	28.3b	(+.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))))

series952.0ms (4.9%)

Counts

4 → 276

Calls

4 calls:

343.0ms	(.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)))))
239.0ms	(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)))
216.0ms	(+.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))))
153.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite165.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`add-sqr-sqrt_binary64`
240×	`log1p-expm1-u_binary64`
240×	`expm1-log1p-u_binary64`
236×	`add-log-exp_binary64`
235×	`add-cube-cbrt_binary64`

Counts

4 → 82

Calls

4 calls:

162.0ms	(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)))
162.0ms	(.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)))))
162.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
162.0ms	(+.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))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	160
1	501	156
2	5088	156

simplify461.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

476×	`associate-r_binary64`
441×	`times-frac_binary64`
329×	`associate-l_binary64`
303×	`fma-neg_binary64`
298×	`associate-/r*_binary64`

Counts

358 → 208

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	307	15852
1	966	15734
2	4857	15734
3	5085	15734

prune480.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	237	11	248
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	238	12	250

Error

30.2b

Counts

250 → 12

Alt Table

Status	Error	Program
	63.3b	(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (.f64 (pow.f64 w 2) h)))))
	59.6b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (.f64 M M))))) (/.f64 c0 (.f64 w 2))))
▶	36.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	44.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) (.f64 w h))) (.f64 (.f64 d d) c0))))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	61.6b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 w (.f64 w h))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	62.3b	(.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)))))
	61.1b	(/.f64 (.f64 (.f64 d d) (.f64 c0 c0)) (.f64 (.f64 D D) (.f64 w (*.f64 w h))))
	63.1b	(exp.f64 (log.f64 (.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (.f64 M M)))) (/.f64 c0 (*.f64 w 2)))))
	50.2b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	62.1b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (pow.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (*.f64 M M)))) 3) 1/3))
	42.8b	(.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 14439 to 6111 computations (57.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	7.1b	(*.f64 (pow.f64 M 2) h)
✓	14.8b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
✓	14.9b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

series163.0ms (0.8%)

Counts

3 → 40

Calls

3 calls:

122.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
28.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
13.0ms	(*.f64 (pow.f64 M 2) h)

rewrite66.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

644×	`log-prod_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
197×	`log-pow_binary64`
119×	`add-sqr-sqrt_binary64`

Counts

3 → 86

Calls

3 calls:

65.0ms	(*.f64 (pow.f64 M 2) h)
65.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
65.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	251	32
2	2898	32
3	5101	32

simplify95.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1383×	`associate-/r/_binary64`
563×	`unswap-sqr_binary64`
511×	`times-frac_binary64`
359×	`associate-/l*_binary64`
214×	`associate-l_binary64`

Counts

126 → 92

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	544
1	29	544
2	80	544
3	346	544
4	2365	544
5	2719	544
6	3302	544
7	3346	544
8	3458	544
9	3600	544
10	5305	544

prune164.0ms (0.8%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	74	18	92
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	80	24	104

Error

16.1b

Counts

104 → 24

Alt Table

Status	Error	Program
	61.6b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 w (.f64 w h))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	43.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (exp.f64 (log.f64 (.f64 (.f64 M M) h)))) (pow.f64 d 2)))
	41.2b	(.f64 1/4 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))
	63.1b	(exp.f64 (log.f64 (.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (.f64 M M)))) (/.f64 c0 (*.f64 w 2)))))
	25.3b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))
	63.3b	(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (.f64 (pow.f64 w 2) h)))))
	24.3b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 h (pow.f64 (.f64 D M) 2))) 2) d) (/.f64 (cbrt.f64 (.f64 h (pow.f64 (.f64 D M) 2))) d)))
	36.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (pow.f64 (cbrt.f64 (.f64 (.f64 M M) h)) 3)) (pow.f64 d 2)))
	27.6b	(.f64 1/4 (/.f64 (pow.f64 (cbrt.f64 (.f64 h (pow.f64 (*.f64 D M) 2))) 3) (pow.f64 d 2)))
	62.1b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (pow.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (*.f64 M M)))) 3) 1/3))
	27.5b	(.f64 1/4 (.f64 (.f64 (pow.f64 (.f64 D M) 2) (neg.f64 h)) (/.f64 1 (neg.f64 (*.f64 d d)))))
	34.5b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 M M) h) d)))
	28.6b	(.f64 1/4 (.f64 (pow.f64 (.f64 D M) 2) (.f64 h (pow.f64 d -2))))
	45.7b	(.f64 1/4 (.f64 (.f64 D (.f64 M (sqrt.f64 h))) (.f64 (.f64 D (*.f64 M (sqrt.f64 h))) (pow.f64 d -2))))
	41.4b	(.f64 1/4 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))))
	41.3b	(.f64 1/4 (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2)) (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2)) 2)))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	41.3b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2)) 3))
	62.3b	(.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)))))
	33.8b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) (cbrt.f64 (pow.f64 d 4))) (/.f64 h (pow.f64 (cbrt.f64 d) 2))))
	48.1b	(.f64 1/4 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))) (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))))))
▶	24.2b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (.f64 h (pow.f64 (.f64 D M) 2)) d)))
	40.5b	(.f64 1/4 (.f64 (/.f64 (.f64 (.f64 M M) h) (cbrt.f64 (pow.f64 d 4))) (/.f64 (*.f64 D D) (pow.f64 (cbrt.f64 d) 2))))
	25.4b	(.f64 1/4 (pow.f64 (.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)) (/.f64 d h)) -1))

Compiler

Compiled 3053 to 1840 computations (39.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 D M) 2)
✓	3.6b	(.f64 (/.f64 1 d) (/.f64 (.f64 h (pow.f64 (*.f64 D M) 2)) d))
✓	5.0b	(/.f64 (.f64 h (pow.f64 (.f64 D M) 2)) d)
✓	5.2b	(.f64 h (pow.f64 (.f64 D M) 2))

series251.0ms (1.3%)

Counts

4 → 156

Calls

4 calls:

158.0ms	(.f64 (/.f64 1 d) (/.f64 (.f64 h (pow.f64 (*.f64 D M) 2)) d))
59.0ms	(/.f64 (.f64 h (pow.f64 (.f64 D M) 2)) d)
26.0ms	(.f64 h (pow.f64 (.f64 D M) 2))
7.0ms	(pow.f64 (*.f64 D M) 2)

rewrite76.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

685×	`log-prod_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
203×	`log-pow_binary64`
158×	`egg-rr`

Counts

4 → 158

Calls

4 calls:

73.0ms	(pow.f64 (*.f64 D M) 2)
73.0ms	(.f64 (/.f64 1 d) (/.f64 (.f64 h (pow.f64 (*.f64 D M) 2)) d))
73.0ms	(/.f64 (.f64 h (pow.f64 (.f64 D M) 2)) d)
73.0ms	(.f64 h (pow.f64 (.f64 D M) 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	271	45
2	3191	45
3	5572	45

simplify226.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

726×	`times-frac_binary64`
537×	`associate-/l*_binary64`
382×	`unswap-sqr_binary64`
367×	`associate-l_binary64`
364×	`sqr-pow_binary64`

Counts

314 → 168

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	2388
1	35	2388
2	107	2388
3	489	2388
4	3388	2388
5	4085	2388
6	4056	2388
7	4177	2388
8	4332	2388
9	4492	2388
10	4636	2388
11	4785	2388
12	4918	2388

prune376.0ms (1.9%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	157	11	168
Fresh	6	17	23
Picked	1	0	1
Done	0	0	0
Total	164	28	192

Error

15.6b

Counts

192 → 28

Alt Table

Status	Error	Program
	34.3b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) d)))
	61.6b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 w (.f64 w h))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	43.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (exp.f64 (log.f64 (.f64 (.f64 M M) h)))) (pow.f64 d 2)))
	41.2b	(.f64 1/4 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))
	42.1b	(.f64 1/4 (.f64 (/.f64 1 d) (.f64 (.f64 (.f64 D M) (sqrt.f64 h)) (.f64 (.f64 (.f64 D M) (sqrt.f64 h)) (/.f64 1 d)))))
	33.8b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) (cbrt.f64 (pow.f64 d 4))) (/.f64 h (pow.f64 (cbrt.f64 d) 2))))
	63.1b	(exp.f64 (log.f64 (.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (.f64 M M)))) (/.f64 c0 (*.f64 w 2)))))
	25.3b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))
▶	24.3b	(.f64 1/4 (.f64 (/.f64 1 d) (.f64 h (/.f64 1 (/.f64 d (pow.f64 (.f64 D M) 2))))))
	63.3b	(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (.f64 (pow.f64 w 2) h)))))
	25.2b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (.f64 h (.f64 D (.f64 M (.f64 D M)))) d)))
	37.5b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (log.f64 (pow.f64 (exp.f64 h) (pow.f64 (*.f64 D M) 2))) d)))
	53.2b	(.f64 1/4 (/.f64 (/.f64 (.f64 (.f64 D M) (sqrt.f64 h)) (sqrt.f64 d)) (/.f64 d (/.f64 (.f64 (*.f64 D M) (sqrt.f64 h)) (sqrt.f64 d)))))
	36.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (pow.f64 (cbrt.f64 (.f64 (.f64 M M) h)) 3)) (pow.f64 d 2)))
	53.8b	(.f64 1/4 (.f64 (/.f64 1 d) (pow.f64 (/.f64 (.f64 (.f64 D M) (sqrt.f64 h)) (sqrt.f64 d)) 2)))
	26.2b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (.f64 h (.f64 M (.f64 D (.f64 D M)))) d)))
	41.4b	(.f64 1/4 (pow.f64 (/.f64 (.f64 (*.f64 D M) (sqrt.f64 h)) d) 2))
	62.1b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (pow.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (*.f64 M M)))) 3) 1/3))
	27.5b	(.f64 1/4 (.f64 (.f64 (pow.f64 (.f64 D M) 2) (neg.f64 h)) (/.f64 1 (neg.f64 (*.f64 d d)))))
	34.5b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 M M) h) d)))
	41.4b	(.f64 1/4 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	41.3b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2)) 3))
	62.3b	(.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)))))
	48.1b	(.f64 1/4 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))) (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))))))
	28.6b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (expm1.f64 (log1p.f64 (.f64 h (pow.f64 (.f64 D M) 2)))) d)))
	24.3b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (pow.f64 (cbrt.f64 (.f64 h (pow.f64 (.f64 D M) 2))) 3) d)))
	45.7b	(.f64 1/4 (.f64 (.f64 D (.f64 M (sqrt.f64 h))) (.f64 (.f64 D (*.f64 M (sqrt.f64 h))) (pow.f64 d -2))))

Compiler

Compiled 4758 to 2913 computations (38.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (/.f64 d (pow.f64 (*.f64 D M) 2)))
✓	3.6b	(.f64 (/.f64 1 d) (.f64 h (/.f64 1 (/.f64 d (pow.f64 (*.f64 D M) 2)))))
✓	5.5b	(/.f64 d (pow.f64 (*.f64 D M) 2))
✓	6.4b	(.f64 h (/.f64 1 (/.f64 d (pow.f64 (.f64 D M) 2))))

series288.0ms (1.5%)

Counts

4 → 168

Calls

4 calls:

108.0ms	(.f64 (/.f64 1 d) (.f64 h (/.f64 1 (/.f64 d (pow.f64 (*.f64 D M) 2)))))
94.0ms	(/.f64 d (pow.f64 (*.f64 D M) 2))
55.0ms	(.f64 h (/.f64 1 (/.f64 d (pow.f64 (.f64 D M) 2))))
31.0ms	(/.f64 1 (/.f64 d (pow.f64 (*.f64 D M) 2)))

rewrite89.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

758×	`log-prod_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
227×	`log-pow_binary64`
155×	`egg-rr`

Counts

4 → 155

Calls

4 calls:

86.0ms	(/.f64 1 (/.f64 d (pow.f64 (*.f64 D M) 2)))
86.0ms	(.f64 (/.f64 1 d) (.f64 h (/.f64 1 (/.f64 d (pow.f64 (*.f64 D M) 2)))))
86.0ms	(/.f64 d (pow.f64 (*.f64 D M) 2))
86.0ms	(.f64 h (/.f64 1 (/.f64 d (pow.f64 (.f64 D M) 2))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	297	49
2	3462	49
3	6056	49

simplify144.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

861×	`times-frac_binary64`
571×	`associate-/l*_binary64`
445×	`unswap-sqr_binary64`
401×	`associate-/r*_binary64`
387×	`associate-l_binary64`

Counts

323 → 165

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	2616
1	41	2616
2	121	2616
3	551	2616
4	3894	2616
5	4711	2616
6	4688	2616
7	4841	2616
8	4935	2616

prune433.0ms (2.2%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	159	6	165
Fresh	5	22	27
Picked	0	1	1
Done	0	0	0
Total	164	29	193

Error

15.4b

Counts

193 → 29

Alt Table

Status	Error	Program
	34.3b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) d)))
	61.6b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 w (.f64 w h))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	43.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (exp.f64 (log.f64 (.f64 (.f64 M M) h)))) (pow.f64 d 2)))
	53.0b	(.f64 1/4 (/.f64 (/.f64 (sqrt.f64 h) (/.f64 (sqrt.f64 d) (.f64 D M))) (/.f64 d (/.f64 (sqrt.f64 h) (/.f64 (sqrt.f64 d) (*.f64 D M))))))
	62.3b	(.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)))))
	33.1b	(.f64 1/4 (.f64 (/.f64 1 d) (.f64 h (/.f64 1 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 d (pow.f64 (.f64 D M) 2)))) (cbrt.f64 (exp.f64 (/.f64 d (pow.f64 (.f64 D M) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 d (pow.f64 (*.f64 D M) 2))))))))))
	33.8b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) (cbrt.f64 (pow.f64 d 4))) (/.f64 h (pow.f64 (cbrt.f64 d) 2))))
	63.1b	(exp.f64 (log.f64 (.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (.f64 M M)))) (/.f64 c0 (*.f64 w 2)))))
	25.3b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))
	33.0b	(.f64 1/4 (.f64 (/.f64 1 d) (.f64 h (/.f64 1 (.f64 (/.f64 (pow.f64 (cbrt.f64 d) 2) (.f64 D D)) (/.f64 (cbrt.f64 d) (.f64 M M)))))))
✓	24.3b	(.f64 1/4 (.f64 (/.f64 1 d) (.f64 h (/.f64 1 (/.f64 d (pow.f64 (.f64 D M) 2))))))
	63.3b	(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (.f64 (pow.f64 w 2) h)))))
	42.5b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (/.f64 h (/.f64 (sqrt.f64 d) (.f64 D M))) (/.f64 (sqrt.f64 d) (.f64 D M)))))
	37.5b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (log.f64 (pow.f64 (exp.f64 h) (pow.f64 (*.f64 D M) 2))) d)))
	53.2b	(.f64 1/4 (/.f64 (/.f64 (.f64 (.f64 D M) (sqrt.f64 h)) (sqrt.f64 d)) (/.f64 d (/.f64 (.f64 (*.f64 D M) (sqrt.f64 h)) (sqrt.f64 d)))))
	26.2b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (.f64 h (.f64 M (.f64 D (.f64 D M)))) d)))
	41.4b	(.f64 1/4 (pow.f64 (/.f64 (.f64 (*.f64 D M) (sqrt.f64 h)) d) 2))
	33.1b	(.f64 1/4 (.f64 (/.f64 1 d) (.f64 h (.f64 (/.f64 (.f64 D D) 1) (/.f64 (.f64 M M) d)))))
	62.1b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (pow.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (*.f64 M M)))) 3) 1/3))
	27.5b	(.f64 1/4 (.f64 (.f64 (pow.f64 (.f64 D M) 2) (neg.f64 h)) (/.f64 1 (neg.f64 (*.f64 d d)))))
	22.0b	(.f64 1/4 (.f64 (/.f64 1 d) (.f64 h (.f64 (/.f64 (.f64 D M) 1) (/.f64 (.f64 D M) d)))))
	34.5b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 M M) h) d)))
	41.4b	(.f64 1/4 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))))
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	41.3b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2)) 3))
	48.1b	(.f64 1/4 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))) (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) d) 2))))))
	53.8b	(.f64 1/4 (.f64 (/.f64 1 d) (pow.f64 (/.f64 (.f64 (.f64 D M) (sqrt.f64 h)) (sqrt.f64 d)) 2)))
	24.3b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (pow.f64 (cbrt.f64 (.f64 h (pow.f64 (.f64 D M) 2))) 3) d)))
	45.7b	(.f64 1/4 (.f64 (.f64 D (.f64 M (sqrt.f64 h))) (.f64 (.f64 D (*.f64 M (sqrt.f64 h))) (pow.f64 d -2))))

Compiler

Compiled 4152 to 2600 computations (37.4% saved)

regimes2.2s (11.4%)

Accuracy

Total 5.9b remaining (29.1%)

Threshold costs 0b (0%)

Counts

163 → 2

Compiler

Compiled 44456 to 31326 computations (29.5% saved)

bsearch193.0ms (1%)

Steps

Iters	Range		Point
10	-1.967233185311223e-302	6.834712372841236e-302	-3.7426609267893e-310

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	43
1	33	43
2	32	43

end481.0ms (2.5%)

Compiler: Compiled 914 to 617 computations (32.5% saved)

Details

analyze2.9s (14.8%)

sample9.1s (47%)

simplify43.0ms (0.2%)

prune6.0ms (0%)

localize18.0ms (0.1%)

series952.0ms (4.9%)

rewrite165.0ms (0.8%)

simplify461.0ms (2.4%)

prune480.0ms (2.5%)

localize10.0ms (0.1%)

series163.0ms (0.8%)

rewrite66.0ms (0.3%)

simplify95.0ms (0.5%)

prune164.0ms (0.8%)

localize12.0ms (0.1%)

series251.0ms (1.3%)

rewrite76.0ms (0.4%)

simplify226.0ms (1.2%)

prune376.0ms (1.9%)

localize11.0ms (0.1%)

series288.0ms (1.5%)

rewrite89.0ms (0.5%)

simplify144.0ms (0.7%)

prune433.0ms (2.2%)

regimes2.2s (11.4%)

bsearch193.0ms (1%)

simplify3.0ms (0%)

end481.0ms (2.5%)

Profiling