Details

analyze2.7s (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)

sample9.3s (46.3%)

Results

3.3s	16342×	body	128	invalid
2.1s	2167×	body	4096	valid
1.5s	1253×	body	8192	valid
1.1s	1287×	body	2048	valid
481.0ms	2454×	body	128	valid
388.0ms	600×	body	1024	valid
156.0ms	340×	body	512	valid
49.0ms	155×	body	256	valid
47.0ms	58×	body	2048	invalid
26.0ms	45×	body	1024	invalid
19.0ms	38×	body	512	invalid
6.0ms	6×	body	8192	exit
6.0ms	7×	body	4096	invalid
4.0ms	12×	body	256	invalid

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify40.0ms (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

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

57.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	60.8b	(.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)))))
▶	58.3b	(.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

60.8b

(*.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)))))

▶

58.3b

(*.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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.2b	(.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)))))
✓	13.6b	(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)))
✓	19.4b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	27.5b	(+.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))))

series1.3s (6.5%)

Counts

4 → 276

Calls

4 calls:

446.0ms	(.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)))))
334.0ms	(+.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))))
301.0ms	(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)))
224.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite50.0ms (0.2%)

Algorithm

2×	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 → 85

Calls

4 calls:

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)))))
46.0ms	(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)))
46.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
46.0ms	(+.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: 0 (0.0ms)

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

simplify311.0ms (1.5%)

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

361 → 211

Iterations

Useful iterations: 1 (0.0ms)

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

prune358.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	244	9	253
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	245	10	255

Error

28.8b

Counts

255 → 10

Alt Table

Status	Error	Program
	60.3b	(cbrt.f64 (pow.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))) 3))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 c0 (.f64 w h)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	60.5b	(/.f64 (.f64 (.f64 d d) (.f64 c0 c0)) (.f64 (.f64 D D) (.f64 w (*.f64 w h))))
	45.9b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	60.8b	(.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)))))
	42.6b	(.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))))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	59.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (*.f64 M M)))) 3)))
	58.1b	(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))))
▶	34.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))

Compiler

Compiled 14524 to 6032 computations (58.5% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	8.0b	(*.f64 (pow.f64 M 2) h)
✓	13.0b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	15.5b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series146.0ms (0.7%)

Counts

3 → 40

Calls

3 calls:

109.0ms	(/.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))
8.0ms	(*.f64 (pow.f64 M 2) h)

rewrite65.0ms (0.3%)

Algorithm

2×	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 → 88

Calls

3 calls:

63.0ms	(*.f64 (pow.f64 M 2) h)
63.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
63.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify111.0ms (0.6%)

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

128 → 94

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

prune191.0ms (0.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	79	15	94
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	82	22	104

Error

15.0b

Counts

104 → 22

Alt Table

Status	Error	Program
	40.0b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2)) 3))
	60.8b	(.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)))))
	34.5b	(.f64 1/4 (.f64 (.f64 (.f64 M M) h) (.f64 (.f64 D D) (pow.f64 d -2))))
	48.6b	(.f64 1/4 (.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) (cbrt.f64 (pow.f64 d 4))) (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) (pow.f64 (cbrt.f64 d) 2))))
	49.2b	(.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))))))
	42.6b	(.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))))
	30.5b	(.f64 1/4 (/.f64 (expm1.f64 (log1p.f64 (.f64 h (pow.f64 (*.f64 D M) 2)))) (pow.f64 d 2)))
	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)))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	33.2b	(.f64 1/4 (.f64 (/.f64 1 (cbrt.f64 (pow.f64 d 4))) (/.f64 (.f64 h (pow.f64 (.f64 D M) 2)) (pow.f64 (cbrt.f64 d) 2))))
	60.3b	(cbrt.f64 (pow.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))) 3))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 c0 (.f64 w h)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	36.8b	(.f64 1/4 (/.f64 (log.f64 (+.f64 1 (expm1.f64 (.f64 h (pow.f64 (*.f64 D M) 2))))) (pow.f64 d 2)))
	24.2b	(.f64 1/4 (.f64 (/.f64 1 d) (/.f64 (.f64 h (pow.f64 (.f64 D M) 2)) d)))
	59.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (*.f64 M M)))) 3)))
	28.6b	(.f64 1/4 (/.f64 (pow.f64 (cbrt.f64 (.f64 h (pow.f64 (*.f64 D M) 2))) 3) (pow.f64 d 2)))
	29.1b	(.f64 1/4 (.f64 (pow.f64 (.f64 D M) 2) (.f64 h (pow.f64 d -2))))
	60.5b	(/.f64 (.f64 (.f64 d d) (.f64 c0 c0)) (.f64 (.f64 D D) (.f64 w (*.f64 w h))))
▶	22.9b	(.f64 1/4 (pow.f64 (.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)) (/.f64 d h)) -1))
	23.0b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))
	39.9b	(.f64 1/4 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))
	30.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 M M) h) d)))

Compiler

Compiled 2947 to 1752 computations (40.5% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 D M) 2)
✓	0.3b	(pow.f64 (.f64 (/.f64 d (pow.f64 (.f64 D M) 2)) (/.f64 d h)) -1)
✓	4.9b	(/.f64 d (pow.f64 (*.f64 D M) 2))
✓	6.5b	(.f64 (/.f64 d (pow.f64 (.f64 D M) 2)) (/.f64 d h))

series678.0ms (3.4%)

Counts

4 → 156

Calls

4 calls:

378.0ms	(pow.f64 (.f64 (/.f64 d (pow.f64 (.f64 D M) 2)) (/.f64 d h)) -1)
169.0ms	(.f64 (/.f64 d (pow.f64 (.f64 D M) 2)) (/.f64 d h))
123.0ms	(/.f64 d (pow.f64 (*.f64 D M) 2))
8.0ms	(pow.f64 (*.f64 D M) 2)

rewrite112.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

454×	`prod-diff_binary64`
238×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
220×	`log-pow_binary64`
177×	`log-div_binary64`

Counts

4 → 145

Calls

4 calls:

109.0ms	(pow.f64 (*.f64 D M) 2)
109.0ms	(pow.f64 (.f64 (/.f64 d (pow.f64 (.f64 D M) 2)) (/.f64 d h)) -1)
109.0ms	(/.f64 d (pow.f64 (*.f64 D M) 2))
109.0ms	(.f64 (/.f64 d (pow.f64 (.f64 D M) 2)) (/.f64 d h))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	283	49
2	3484	49
3	4990	49
4	5884	49
0	0	0
1	0	0

simplify253.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

561×	`associate-/r*_binary64`
560×	`associate-/l*_binary64`
407×	`associate-l_binary64`
389×	`sqr-pow_binary64`
307×	`associate-r_binary64`

Counts

301 → 154

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	2532
1	38	2532
2	126	2532
3	599	2532
4	3341	2532
5	3882	2532
6	3860	2532
7	3996	2532
8	4159	2532
9	4326	2532
10	4474	2532
11	4634	2532
12	4873	2532
13	4909	2532
14	4909	2532

prune439.0ms (2.2%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	138	16	154
Fresh	9	12	21
Picked	1	0	1
Done	0	0	0
Total	148	28	176

Error

13.6b

Counts

176 → 28

Alt Table

Status	Error	Program
	24.7b	(.f64 1/4 (pow.f64 (/.f64 (.f64 d (/.f64 d (pow.f64 (*.f64 D M) 2))) h) -1))
	23.7b	(.f64 1/4 (pow.f64 (.f64 (/.f64 d (.f64 D (.f64 M (*.f64 D M)))) (/.f64 d h)) -1))
	60.5b	(/.f64 (.f64 (.f64 d d) (.f64 c0 c0)) (.f64 (.f64 D D) (.f64 w (*.f64 w h))))
	30.7b	(.f64 1/4 (pow.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)) 3) 1/3) (/.f64 d h)) -1))
	22.4b	(.f64 1/4 (pow.f64 (/.f64 d (/.f64 (pow.f64 (.f64 D M) 2) (/.f64 d h))) -1))
	20.2b	(.f64 1/4 (pow.f64 (.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 d) 2) (.f64 D M)) (/.f64 (cbrt.f64 d) (*.f64 D M))) (/.f64 d h)) -1))
	40.0b	(.f64 1/4 (pow.f64 (.f64 (/.f64 d (exp.f64 (.f64 2 (log.f64 (.f64 D M))))) (/.f64 d h)) -1))
	60.8b	(.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)))))
	34.5b	(.f64 1/4 (.f64 (.f64 (.f64 M M) h) (.f64 (.f64 D D) (pow.f64 d -2))))
▶	20.0b	(.f64 1/4 (pow.f64 (.f64 (.f64 (/.f64 1 (.f64 D M)) (/.f64 d (*.f64 D M))) (/.f64 d h)) -1))
	23.2b	(.f64 1/4 (pow.f64 (.f64 (/.f64 d (expm1.f64 (log1p.f64 (pow.f64 (*.f64 D M) 2)))) (/.f64 d h)) -1))
	48.6b	(.f64 1/4 (.f64 (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) (cbrt.f64 (pow.f64 d 4))) (/.f64 (.f64 D (.f64 M (sqrt.f64 h))) (pow.f64 (cbrt.f64 d) 2))))
	49.2b	(.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))))))
	42.6b	(.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))))
	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)))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.3b	(cbrt.f64 (pow.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))) 3))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 c0 (.f64 w h)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	23.1b	(.f64 1/4 (pow.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 d) 2) (.f64 (cbrt.f64 d) (pow.f64 (*.f64 D M) -2))) (/.f64 d h)) -1))
	59.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (*.f64 M M)))) 3)))
	44.4b	(.f64 1/4 (pow.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)))) 1) (/.f64 d h)) -1))
	27.7b	(.f64 1/4 (exp.f64 (log.f64 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))))
	32.1b	(.f64 1/4 (log.f64 (pow.f64 (exp.f64 (/.f64 (pow.f64 (.f64 D M) 2) d)) (/.f64 h d))))
	39.9b	(.f64 1/4 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))
	32.2b	(.f64 1/4 (pow.f64 (.f64 (log.f64 (exp.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)))) (/.f64 d h)) -1))
	24.5b	(.f64 1/4 (.f64 (/.f64 1 (.f64 d (/.f64 d (pow.f64 (.f64 D M) 2)))) h))
	32.7b	(.f64 1/4 (pow.f64 (/.f64 (/.f64 (.f64 d (/.f64 d h)) (.f64 D D)) (.f64 M M)) -1))
	22.9b	(.f64 1/4 (pow.f64 (/.f64 (/.f64 (.f64 d (/.f64 d h)) (.f64 D M)) (.f64 D M)) -1))

Compiler

Compiled 4379 to 2609 computations (40.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (.f64 (.f64 (/.f64 1 (.f64 D M)) (/.f64 d (.f64 D M))) (/.f64 d h)) -1)
✓	0.3b	(/.f64 1 (*.f64 D M))
✓	4.4b	(/.f64 d (*.f64 D M))
✓	6.5b	(.f64 (.f64 (/.f64 1 (.f64 D M)) (/.f64 d (.f64 D M))) (/.f64 d h))

series777.0ms (3.9%)

Counts

4 → 96

Calls

4 calls:

542.0ms	(pow.f64 (.f64 (.f64 (/.f64 1 (.f64 D M)) (/.f64 d (.f64 D M))) (/.f64 d h)) -1)
183.0ms	(.f64 (.f64 (/.f64 1 (.f64 D M)) (/.f64 d (.f64 D M))) (/.f64 d h))
44.0ms	(/.f64 d (*.f64 D M))
8.0ms	(/.f64 1 (*.f64 D M))

rewrite164.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
147×	`egg-rr`
147×	`add-sqr-sqrt_binary64`
135×	`add-cbrt-cube_binary64`

Counts

4 → 147

Calls

4 calls:

130.0ms	(pow.f64 (.f64 (.f64 (/.f64 1 (.f64 D M)) (/.f64 d (.f64 D M))) (/.f64 d h)) -1)
130.0ms	(/.f64 1 (*.f64 D M))
130.0ms	(/.f64 d (*.f64 D M))
130.0ms	(.f64 (.f64 (/.f64 1 (.f64 D M)) (/.f64 d (.f64 D M))) (/.f64 d h))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	300	43
2	3950	43
3	4972	43
4	4931	43
0	0	0
1	0	0

simplify217.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

893×	`*-commutative_binary64`
534×	`sqr-pow_binary64`
516×	`associate-/l*_binary64`
468×	`associate-/r*_binary64`
329×	`associate-l_binary64`

Counts

243 → 153

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	1824
1	34	1824
2	115	1824
3	545	1824
4	2992	1824
5	3369	1824
6	3376	1824
7	3499	1824
8	3640	1824
9	3796	1824
10	4070	1824
11	4224	1824
12	4450	1824
13	4702	1824
14	4991	1824
15	4895	1824

prune537.0ms (2.7%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	140	13	153
Fresh	8	19	27
Picked	1	0	1
Done	0	0	0
Total	149	32	181

Error

13.1b

Counts

181 → 32

Alt Table

Status	Error	Program
	50.5b	(.f64 1/4 (pow.f64 (.f64 (.f64 (/.f64 1 (.f64 D M)) (exp.f64 (fma.f64 -1 (log.f64 (*.f64 D M)) (log.f64 d)))) (/.f64 d h)) -1))
	60.5b	(/.f64 (.f64 (.f64 d d) (.f64 c0 c0)) (.f64 (.f64 D D) (.f64 w (*.f64 w h))))
	30.7b	(.f64 1/4 (pow.f64 (.f64 (pow.f64 (pow.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)) 3) 1/3) (/.f64 d h)) -1))
	27.7b	(.f64 1/4 (exp.f64 (log.f64 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))))
	18.5b	(.f64 1/4 (/.f64 (.f64 D M) (.f64 (/.f64 d (.f64 D M)) (/.f64 d h))))
	20.2b	(.f64 1/4 (pow.f64 (.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 d) 2) (.f64 D M)) (/.f64 (cbrt.f64 d) (*.f64 D M))) (/.f64 d h)) -1))
	20.5b	(.f64 1/4 (pow.f64 (/.f64 (.f64 (/.f64 d (.f64 D M)) d) (.f64 (*.f64 D M) h)) -1))
	26.1b	(.f64 1/4 (pow.f64 (.f64 (.f64 (/.f64 1 (.f64 D M)) (.f64 (cbrt.f64 (.f64 d d)) (.f64 (cbrt.f64 d) (/.f64 1 (.f64 D M))))) (/.f64 d h)) -1))
	60.8b	(.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)))))
	34.5b	(.f64 1/4 (.f64 (.f64 (.f64 M M) h) (.f64 (.f64 D D) (pow.f64 d -2))))
	19.1b	(.f64 1/4 (pow.f64 (/.f64 (/.f64 d (.f64 D M)) (.f64 (.f64 D M) (/.f64 h d))) -1))
	18.7b	(.f64 1/4 (pow.f64 (/.f64 (.f64 (/.f64 d (.f64 D M)) (/.f64 d h)) (.f64 D M)) -1))
	23.2b	(.f64 1/4 (pow.f64 (.f64 (/.f64 d (expm1.f64 (log1p.f64 (pow.f64 (*.f64 D M) 2)))) (/.f64 d h)) -1))
	49.2b	(.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))))))
	24.0b	(.f64 1/4 (pow.f64 (.f64 (.f64 (/.f64 1 (.f64 D M)) (cbrt.f64 (pow.f64 (/.f64 d (*.f64 D M)) 3))) (/.f64 d h)) -1))
	42.6b	(.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))))
	28.8b	(.f64 1/4 (pow.f64 (.f64 (.f64 (/.f64 1 (.f64 D M)) (pow.f64 (pow.f64 (/.f64 d (*.f64 D M)) 3) 1/3)) (/.f64 d h)) -1))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	23.1b	(.f64 1/4 (pow.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 d) 2) (.f64 (cbrt.f64 d) (pow.f64 (*.f64 D M) -2))) (/.f64 d h)) -1))
	18.5b	(.f64 1/4 (.f64 (pow.f64 (/.f64 1 (.f64 D M)) -1) (pow.f64 (.f64 (/.f64 d (*.f64 D M)) (/.f64 d h)) -1)))
	20.2b	(.f64 1/4 (pow.f64 (/.f64 (pow.f64 (/.f64 d (.f64 D M)) 2) h) -1))
	60.3b	(cbrt.f64 (pow.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))) 3))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 c0 (.f64 w h)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	59.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 2) (*.f64 M M)))) 3)))
	44.4b	(.f64 1/4 (pow.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)))) 1) (/.f64 d h)) -1))
	20.0b	(.f64 1/4 (.f64 (/.f64 1 (pow.f64 (/.f64 d (*.f64 D M)) 2)) h))
	33.4b	(.f64 1/4 (pow.f64 (.f64 (.f64 (pow.f64 (pow.f64 (/.f64 1 (.f64 D M)) 3) 1/3) (/.f64 d (*.f64 D M))) (/.f64 d h)) -1))
	32.2b	(.f64 1/4 (pow.f64 (.f64 (log.f64 (exp.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)))) (/.f64 d h)) -1))
	34.5b	(.f64 1/4 (pow.f64 (.f64 (.f64 (log.f64 (exp.f64 (/.f64 1 (.f64 D M)))) (/.f64 d (*.f64 D M))) (/.f64 d h)) -1))
	32.1b	(.f64 1/4 (log.f64 (pow.f64 (exp.f64 (/.f64 (pow.f64 (.f64 D M) 2) d)) (/.f64 h d))))
	39.9b	(.f64 1/4 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))
	24.5b	(.f64 1/4 (.f64 (/.f64 1 (.f64 d (/.f64 d (pow.f64 (.f64 D M) 2)))) h))

Compiler

Compiled 4007 to 2172 computations (45.8% saved)

regimes1.8s (9%)

Accuracy

Total 6.4b remaining (32.8%)

Threshold costs 0b (0%)

Counts

153 → 3

Compiler

Compiled 46504 to 31017 computations (33.3% saved)

bsearch7.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	87
1	42	87
2	41	87

end436.0ms (2.2%)

Compiler: Compiled 1021 to 675 computations (33.9% saved)

Details

analyze2.7s (13.5%)

sample9.3s (46.3%)

simplify40.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series1.3s (6.5%)

rewrite50.0ms (0.2%)

simplify311.0ms (1.5%)

prune358.0ms (1.8%)

localize9.0ms (0%)

series146.0ms (0.7%)

rewrite65.0ms (0.3%)

simplify111.0ms (0.6%)

prune191.0ms (0.9%)

localize10.0ms (0%)

series678.0ms (3.4%)

rewrite112.0ms (0.6%)

simplify253.0ms (1.3%)

prune439.0ms (2.2%)

localize11.0ms (0.1%)

series777.0ms (3.9%)

rewrite164.0ms (0.8%)

simplify217.0ms (1.1%)

prune537.0ms (2.7%)

regimes1.8s (9%)

bsearch7.0ms (0%)

simplify3.0ms (0%)

end436.0ms (2.2%)

Profiling