Details

analyze2.5s (10.6%)

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)

sample9.0s (37.6%)

Results

3.2s	16928×	body	128	invalid
2.0s	2152×	body	4096	valid
1.4s	1182×	body	8192	valid
986.0ms	1305×	body	2048	valid
493.0ms	2481×	body	128	valid
425.0ms	683×	body	1024	valid
141.0ms	302×	body	512	valid
48.0ms	151×	body	256	valid
47.0ms	59×	body	2048	invalid
36.0ms	60×	body	1024	invalid
20.0ms	44×	body	512	invalid
10.0ms	10×	body	8192	exit
8.0ms	9×	body	4096	invalid
6.0ms	19×	body	256	invalid

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify54.0ms (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

prune9.0ms (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

60.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	60.9b	(.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)))))
	62.8b	(.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)))))

Status

Error

Program

▶

60.9b

(*.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)))))

62.8b

(*.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)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.9b	(.f64 (.f64 w h) (*.f64 D D))
✓	14.3b	(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)))
✓	17.9b	(/.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))))

series1.4s (6%)

Counts

4 → 240

Calls

4 calls:

545.0ms	(+.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))))
510.0ms	(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)))
328.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
50.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite143.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

791×	`prod-diff_binary64`
203×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
191×	`add-log-exp_binary64`

Counts

4 → 128

Calls

4 calls:

136.0ms	(.f64 (.f64 w h) (*.f64 D D))
136.0ms	(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)))
135.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
135.0ms	(+.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	18	110
1	405	108
2	4795	108
3	6251	108
0	0	0
1	0	0

simplify593.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-def_binary64`
505×	`unswap-sqr_binary64`
293×	`associate-r_binary64`
261×	`fma-neg_binary64`
256×	`times-frac_binary64`

Counts

368 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	11169
1	648	11085
2	3136	11033
3	4940	11033
4	4979	11033
5	4998	11033
6	4980	11033

prune1.0s (4.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	362	8	370
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	363	9	372

Error

37.0b

Counts

372 → 9

Alt Table

Status	Error	Program
	60.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	43.2b	(.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))))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) (pow.f64 (cbrt.f64 (.f64 (.f64 w h) (.f64 D D))) 2)) (/.f64 d (cbrt.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)))))
▶	42.7b	(.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))))
	52.5b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	62.1b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.f64 (.f64 w h) (.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)))))
	62.8b	(.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)))))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 d d) (.f64 (.f64 w h) D)) (/.f64 c0 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)))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) (.f64 D (sqrt.f64 (.f64 w h)))) (/.f64 d (.f64 D (sqrt.f64 (.f64 w h))))) (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 21927 to 6306 computations (71.2% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.4b	(*.f64 (pow.f64 d 2) c0)
✓	12.7b	(.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))))
✓	16.6b	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
✓	16.6b	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))

series1.1s (4.5%)

Counts

4 → 144

Calls

4 calls:

494.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))
474.0ms	(.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))))
104.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
13.0ms	(*.f64 (pow.f64 d 2) c0)

rewrite130.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 102

Calls

4 calls:

125.0ms	(*.f64 (pow.f64 d 2) c0)
125.0ms	(.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))))
125.0ms	(.f64 (pow.f64 D 2) (.f64 w (*.f64 h (pow.f64 M 2))))
125.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (.f64 (pow.f64 d 2) c0))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	85
1	451	80
2	4846	80
3	4966	80
0	0	0
1	0	0

simplify224.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

769×	`associate-*l/_binary64`
612×	`associate-/l/_binary64`
577×	`associate-/r/_binary64`
546×	`associate-*r/_binary64`
283×	`unswap-sqr_binary64`

Counts

246 → 109

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	3096
1	56	3096
2	224	3096
3	1427	3096
4	4578	3096
5	4783	3096
6	5125	3096

prune358.0ms (1.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	94	15	109
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	97	21	118

Error

25.5b

Counts

118 → 21

Alt Table

Status	Error	Program
	60.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (*.f64 d (sqrt.f64 c0))) 2)) 3)))
	49.4b	(/.f64 (.f64 1 (.f64 1/2 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2))) (.f64 (/.f64 (.f64 2 w) c0) (.f64 (*.f64 d d) c0)))
	49.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 (.f64 (.f64 D D) w) (.f64 d (sqrt.f64 c0))) (/.f64 (.f64 h (.f64 M M)) (.f64 d (sqrt.f64 c0))))))
	47.8b	(/.f64 (.f64 c0 (.f64 1/2 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2))) (.f64 (.f64 2 w) (.f64 (*.f64 d d) c0)))
	48.6b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (pow.f64 (cbrt.f64 (.f64 (.f64 d d) c0)) 2)) (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (cbrt.f64 (.f64 (.f64 d d) c0))))))
	49.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2))) (*.f64 (pow.f64 d 2) c0))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 1 (.f64 d (sqrt.f64 c0))) (/.f64 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2) (*.f64 d (sqrt.f64 c0))))))
	49.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 (.f64 D D) (.f64 d (sqrt.f64 c0))) (/.f64 (.f64 w (.f64 h (.f64 M M))) (.f64 d (sqrt.f64 c0))))))
	62.8b	(.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)))))
▶	36.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) (.f64 D (sqrt.f64 (.f64 w h)))) (/.f64 d (.f64 D (sqrt.f64 (.f64 w h))))) (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)))))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) (pow.f64 (cbrt.f64 (.f64 (.f64 w h) (.f64 D D))) 2)) (/.f64 d (cbrt.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)))))
	61.5b	(exp.f64 (log.f64 (.f64 (/.f64 c0 (.f64 2 w)) (.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (*.f64 d (sqrt.f64 c0))) 2) 1/2))))
	49.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (pow.f64 (/.f64 (.f64 (.f64 d d) c0) (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2)) -1)))
	45.6b	(log.f64 (pow.f64 (exp.f64 (/.f64 c0 (.f64 2 w))) (.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (.f64 d (sqrt.f64 c0))) 2) 1/2)))
	52.5b	(.f64 (/.f64 c0 (.f64 2 w)) (sqrt.f64 (neg.f64 (pow.f64 M 2))))
	48.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (.f64 d d)) (/.f64 (.f64 D (.f64 (sqrt.f64 (*.f64 w h)) M)) c0))))
	51.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2) 3) 1/3) (*.f64 (pow.f64 d 2) c0))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (log.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (*.f64 d (sqrt.f64 c0))) 2)))))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 d d) (.f64 (.f64 w h) D)) (/.f64 c0 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 4588 to 2317 computations (49.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
✓	6.4b	(*.f64 (pow.f64 M 2) h)
✓	15.6b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	18.2b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series574.0ms (2.4%)

Counts

4 → 72

Calls

4 calls:

267.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
232.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
55.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
19.0ms	(*.f64 (pow.f64 M 2) h)

rewrite169.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

736×	`log-prod_binary64`
242×	`expm1-udef_binary64`
242×	`log1p-udef_binary64`
222×	`log-pow_binary64`
137×	`add-sqr-sqrt_binary64`

Counts

4 → 113

Calls

4 calls:

165.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
165.0ms	(*.f64 (pow.f64 M 2) h)
165.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
165.0ms	(/.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	14	61
1	295	50
2	3380	50
3	5861	50
0	0	0
1	0	0

simplify158.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

865×	`times-frac_binary64`
578×	`associate-/l*_binary64`
565×	`unswap-sqr_binary64`
407×	`associate-r_binary64`
397×	`associate-l_binary64`

Counts

185 → 121

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	1248
1	34	1248
2	101	1248
3	511	1248
4	4017	1248
5	4375	1248
6	4953	1248
7	4942	1248
8	5016	1248

prune402.0ms (1.7%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	108	13	121
Fresh	6	14	20
Picked	1	0	1
Done	0	0	0
Total	115	27	142

Error

15.6b

Counts

142 → 27

Alt Table

Status	Error	Program
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) (pow.f64 (cbrt.f64 (.f64 (.f64 w h) (.f64 D D))) 2)) (/.f64 d (cbrt.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)))))
	39.6b	(.f64 1/4 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))
	44.1b	(.f64 1/4 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2) 3)))
	32.4b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 M M) h) d)))
	61.5b	(exp.f64 (log.f64 (.f64 (/.f64 c0 (.f64 2 w)) (.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (*.f64 d (sqrt.f64 c0))) 2) 1/2))))
	60.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (*.f64 d (sqrt.f64 c0))) 2)) 3)))
	39.7b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2)) 3))
	48.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (.f64 d d)) (/.f64 (.f64 D (.f64 (sqrt.f64 (*.f64 w h)) M)) c0))))
	23.9b	(/.f64 1/4 (.f64 (/.f64 d (pow.f64 (.f64 D M) 2)) (/.f64 d h)))
	49.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2))) (*.f64 (pow.f64 d 2) c0))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 1 (.f64 d (sqrt.f64 c0))) (/.f64 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2) (*.f64 d (sqrt.f64 c0))))))
	62.8b	(.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)))))
	44.8b	(.f64 1/4 (/.f64 (pow.f64 (.f64 D (*.f64 M (sqrt.f64 h))) 2) (pow.f64 d 2)))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (log.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (*.f64 d (sqrt.f64 c0))) 2)))))
	39.7b	(pow.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2) 1/4)) 3)
	25.5b	(.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)))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 d d) (.f64 (.f64 w h) D)) (/.f64 c0 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)))))
	34.4b	(.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))))
	29.1b	(.f64 1/4 (.f64 (pow.f64 (.f64 D M) 2) (.f64 h (pow.f64 d -2))))
	29.7b	(.f64 1/4 (.f64 (.f64 (pow.f64 (.f64 D M) 2) (neg.f64 h)) (/.f64 1 (neg.f64 (*.f64 d d)))))
	49.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (pow.f64 (/.f64 (.f64 (.f64 d d) c0) (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2)) -1)))
	45.6b	(log.f64 (pow.f64 (exp.f64 (/.f64 c0 (.f64 2 w))) (.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (.f64 d (sqrt.f64 c0))) 2) 1/2)))
▶	23.8b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))
	51.7b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2) 3) 1/3) (*.f64 (pow.f64 d 2) c0))))
	35.0b	(.f64 1/4 (/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 h (pow.f64 (*.f64 D M) 2)))) 1) (pow.f64 d 2)))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) (.f64 D (sqrt.f64 (.f64 w h)))) (/.f64 d (.f64 D (sqrt.f64 (.f64 w h))))) (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 3846 to 2225 computations (42.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))
✓	0.2b	(pow.f64 (*.f64 D M) 2)
✓	7.0b	(/.f64 (pow.f64 (*.f64 D M) 2) d)
✓	8.3b	(.f64 (/.f64 (pow.f64 (.f64 D M) 2) d) (/.f64 h d))

series544.0ms (2.3%)

Counts

4 → 156

Calls

4 calls:

236.0ms	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))
200.0ms	(.f64 (/.f64 (pow.f64 (.f64 D M) 2) d) (/.f64 h d))
94.0ms	(/.f64 (pow.f64 (*.f64 D M) 2) d)
13.0ms	(pow.f64 (*.f64 D M) 2)

rewrite128.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

737×	`log-prod_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
212×	`log-pow_binary64`
155×	`log-div_binary64`

Counts

4 → 142

Calls

4 calls:

123.0ms	(.f64 1/4 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))
123.0ms	(pow.f64 (*.f64 D M) 2)
123.0ms	(/.f64 (pow.f64 (*.f64 D M) 2) d)
123.0ms	(.f64 (/.f64 (pow.f64 (.f64 D M) 2) d) (/.f64 h d))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	282	52
2	3462	52
3	6031	52
0	0	0
1	0	0

simplify215.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

748×	`associate-/l*_binary64`
601×	`associate-l_binary64`
590×	`associate-r_binary64`
413×	`associate-/r*_binary64`
307×	`unswap-sqr_binary64`

Counts

298 → 151

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	2676
1	40	2676
2	127	2676
3	649	2676
4	4204	2676
5	4750	2676
6	4724	2676
7	4860	2676
8	4955	2676

prune565.0ms (2.4%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	141	10	151
Fresh	9	17	26
Picked	1	0	1
Done	0	0	0
Total	151	27	178

Error

14.4b

Counts

178 → 27

Alt Table

Status	Error	Program
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) (pow.f64 (cbrt.f64 (.f64 (.f64 w h) (.f64 D D))) 2)) (/.f64 d (cbrt.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)))))
	39.6b	(.f64 1/4 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2))
	32.4b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 M M) h) d)))
	61.5b	(exp.f64 (log.f64 (.f64 (/.f64 c0 (.f64 2 w)) (.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (*.f64 d (sqrt.f64 c0))) 2) 1/2))))
	31.2b	(log.f64 (pow.f64 (pow.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d)) (/.f64 h d)) 1/4))
	49.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (pow.f64 (/.f64 (.f64 (.f64 d d) c0) (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2)) -1)))
	60.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	20.2b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D M) (pow.f64 (cbrt.f64 d) 2)) (/.f64 (*.f64 D M) (cbrt.f64 d))) (/.f64 h d)))
	20.1b	(.f64 1/4 (.f64 (.f64 (.f64 D M) (.f64 (.f64 D M) (/.f64 1 d))) (/.f64 h d)))
	39.7b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D (*.f64 M (sqrt.f64 h))) d) 2)) 3))
	49.4b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (exp.f64 (log.f64 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2))) (*.f64 (pow.f64 d 2) c0))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 1 (.f64 d (sqrt.f64 c0))) (/.f64 (pow.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) 2) (*.f64 d (sqrt.f64 c0))))))
	42.2b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 (*.f64 D M) 2) (/.f64 h d)) (sqrt.f64 d)) (sqrt.f64 d)))
	25.1b	(.f64 1/4 (.f64 (/.f64 (.f64 M (.f64 D (*.f64 D M))) d) (/.f64 h d)))
	24.6b	(.f64 1/4 (/.f64 h (.f64 (/.f64 d (pow.f64 (*.f64 D M) 2)) d)))
	62.8b	(.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)))))
	44.8b	(.f64 1/4 (/.f64 (pow.f64 (.f64 D (*.f64 M (sqrt.f64 h))) 2) (pow.f64 d 2)))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (exp.f64 (log.f64 (pow.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (*.f64 d (sqrt.f64 c0))) 2)))))
	25.5b	(.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)))
	28.3b	(.f64 1/4 (exp.f64 (log.f64 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) (/.f64 h d)))))
	24.2b	(.f64 1/4 (.f64 (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (*.f64 D M) 2))) d) (/.f64 h d)))
	35.7b	(.f64 1/4 (.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 D M) 2) 3) (pow.f64 d 3))) (/.f64 h d)))
	35.0b	(.f64 1/4 (/.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 h (pow.f64 (*.f64 D M) 2)))) 1) (pow.f64 d 2)))
	24.1b	(/.f64 (.f64 (.f64 (/.f64 (pow.f64 (*.f64 D M) 2) d) 1/4) h) d)
	48.1b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (/.f64 (.f64 D (.f64 (sqrt.f64 (.f64 w h)) M)) (.f64 d d)) (/.f64 (.f64 D (.f64 (sqrt.f64 (*.f64 w h)) M)) c0))))
	61.6b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 d d) (.f64 (.f64 w h) D)) (/.f64 c0 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)))))
	63.2b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (/.f64 (.f64 c0 d) (.f64 D (sqrt.f64 (.f64 w h)))) (/.f64 d (.f64 D (sqrt.f64 (.f64 w h))))) (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 3417 to 1855 computations (45.7% saved)

regimes3.6s (14.8%)

Accuracy

Total 4.8b remaining (24.7%)

Threshold costs 0b (0%)

Counts

126 → 2

Compiler

Compiled 39440 to 25719 computations (34.8% saved)

bsearch255.0ms (1.1%)

Steps

Iters	Range		Point
9	-2.76452924359683e-303	3.528714073809127e-309	-2.062391211447e-312

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	49
1	35	49
2	34	49

end718.0ms (3%)

Compiler: Compiled 900 to 574 computations (36.2% saved)

Details

analyze2.5s (10.6%)

sample9.0s (37.6%)

simplify54.0ms (0.2%)

prune9.0ms (0%)

localize41.0ms (0.2%)

series1.4s (6%)

rewrite143.0ms (0.6%)

simplify593.0ms (2.5%)

prune1.0s (4.2%)

localize33.0ms (0.1%)

series1.1s (4.5%)

rewrite130.0ms (0.5%)

simplify224.0ms (0.9%)

prune358.0ms (1.5%)

localize18.0ms (0.1%)

series574.0ms (2.4%)

rewrite169.0ms (0.7%)

simplify158.0ms (0.7%)

prune402.0ms (1.7%)

localize16.0ms (0.1%)

series544.0ms (2.3%)

rewrite128.0ms (0.5%)

simplify215.0ms (0.9%)

prune565.0ms (2.4%)

regimes3.6s (14.8%)

bsearch255.0ms (1.1%)

simplify5.0ms (0%)

end718.0ms (3%)

Profiling