Details

analyze2.5s (16.2%)

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)

sample8.5s (55.1%)

Results

3.0s	16356×	body	128	invalid
2.0s	2193×	body	4096	valid
1.4s	1202×	body	8192	valid
1.0s	1351×	body	2048	valid
459.0ms	2421×	body	128	valid
386.0ms	630×	body	1024	valid
134.0ms	304×	body	512	valid
54.0ms	75×	body	2048	invalid
53.0ms	155×	body	256	valid
37.0ms	49×	body	1024	invalid
15.0ms	32×	body	512	invalid
9.0ms	11×	body	4096	invalid
9.0ms	9×	body	8192	exit
7.0ms	15×	body	256	invalid

Compiler

Compiled 118 to 44 computations (62.7% saved)

preprocess47.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

506×	`times-frac_binary64`
396×	`fma-neg_binary64`
336×	`associate-/r*_binary64`
250×	`associate-*r/_binary64`
250×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	159	1248
1	726	1184
2	4095	1184
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 58 to 21 computations (63.8% saved)

simplify30.0ms (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

59.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	63.3b	(.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)))))
▶	59.9b	(.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)))))

Status

Error

Program

63.3b

(*.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)))))

▶

59.9b

(*.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)))))

Compiler

Compiled 321 to 134 computations (58.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	13.1b	(.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)))))
✓	13.8b	(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)))
✓	15.0b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	29.6b	(+.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))))

series858.0ms (5.5%)

Counts

4 → 276

Calls

69 calls:

54.0ms	(.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)))))	d	inf
32.0ms	(.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)))))	d	-inf
27.0ms	(.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)))))	D	0
22.0ms	(+.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))))	d	inf
22.0ms	(.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)))))	c0	-inf

rewrite54.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`add-sqr-sqrt_binary64`
240×	`log1p-expm1-u_binary64`
240×	`expm1-log1p-u_binary64`
239×	`add-cbrt-cube_binary64`
236×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	160
1	503	156

Stop Event

1×	node limit

Counts

4 → 82

simplify171.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-r_binary64`
441×	`times-frac_binary64`
330×	`associate-l_binary64`
298×	`associate-/r*_binary64`
266×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	307	15852
1	1180	15734

Stop Event

1×	node limit

Counts

358 → 208

prune355.0ms (2.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	236	12	248
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	238	12	250

Error

17.2b

Counts

250 → 12

Alt Table

Status	Error	Program
	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)))))
	50.4b	(log.f64 (pow.f64 (exp.f64 (/.f64 c0 (.f64 w 2))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (*.f64 M M))))))
	61.0b	(.f64 (/.f64 (.f64 c0 c0) (.f64 D D)) (/.f64 (.f64 d d) (.f64 w (.f64 w h))))
	61.3b	(/.f64 (.f64 c0 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M))))) (.f64 w 2))
	60.9b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	59.7b	(fma.f64 (.f64 (/.f64 d D) (/.f64 d D)) (.f64 (/.f64 c0 h) (/.f64 c0 (.f64 w w))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h))) -1/4))
	36.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	38.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 h (.f64 w (.f64 M M))) c0))))
	57.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	52.2b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
▶	25.6b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (*.f64 M h))))
	61.8b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) 3/2))))

Compiler

Compiled 14337 to 6041 computations (57.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 M (.f64 M h))
✓	0.3b	(*.f64 (/.f64 D d) (/.f64 D d))
✓	14.7b	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))

series129.0ms (0.8%)

Counts

3 → 96

Calls

24 calls:

11.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))	h	-inf
11.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))	h	0
10.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))	D	0
9.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))	M	-inf
9.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))	D	-inf

rewrite50.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`log-prod_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
176×	`log-pow_binary64`
125×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	212	29
2	2920	29

Stop Event

1×	node limit

Counts

3 → 82

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
444×	`associate-/l*_binary64`
295×	`associate-l_binary64`
293×	`unswap-sqr_binary64`
236×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	1320
1	37	1320
2	105	1320
3	464	1320
4	3703	1320
5	4269	1320
6	4363	1320
7	4510	1320
8	4674	1320
9	4852	1320

Stop Event

1×	node limit

Counts

178 → 90

prune138.0ms (0.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	74	16	90
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	78	24	102

Error

12.2b

Counts

102 → 24

Alt Table

Status	Error	Program
	57.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	33.1b	(.f64 1/4 (.f64 (/.f64 1 (/.f64 (.f64 d d) (.f64 D D))) (.f64 M (.f64 M h))))
	29.9b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	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)))))
	50.4b	(log.f64 (pow.f64 (exp.f64 (/.f64 c0 (.f64 w 2))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (*.f64 M M))))))
	26.1b	(.f64 1/4 (.f64 (/.f64 1 (.f64 (/.f64 d D) (/.f64 d D))) (.f64 M (*.f64 M h))))
	61.0b	(.f64 (/.f64 (.f64 c0 c0) (.f64 D D)) (/.f64 (.f64 d d) (.f64 w (.f64 w h))))
	61.3b	(/.f64 (.f64 c0 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M))))) (.f64 w 2))
	25.8b	(.f64 1/4 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 D d)) 2) 3) (.f64 M (.f64 M h))))
	27.4b	(.f64 1/4 (.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (*.f64 M h))))
	60.9b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	59.7b	(fma.f64 (.f64 (/.f64 d D) (/.f64 d D)) (.f64 (/.f64 c0 h) (/.f64 c0 (.f64 w w))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h))) -1/4))
	32.3b	(.f64 1/4 (.f64 (pow.f64 (pow.f64 (pow.f64 (/.f64 D d) 2) 3) 1/3) (.f64 M (.f64 M h))))
	43.9b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (pow.f64 (.f64 M (sqrt.f64 h)) 2)))
	45.8b	(.f64 1/4 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2) 3)))
	27.2b	(.f64 1/4 (.f64 (/.f64 (/.f64 (.f64 D (/.f64 D d)) (pow.f64 (cbrt.f64 d) 2)) (cbrt.f64 d)) (.f64 M (*.f64 M h))))
	31.1b	(.f64 1/4 (/.f64 (.f64 (.f64 D (/.f64 D d)) (.f64 h (*.f64 M M))) d))
▶	25.7b	(.f64 1/4 (.f64 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))) (.f64 M (.f64 M h))))
	31.7b	(.f64 1/4 (.f64 (.f64 D (/.f64 D (.f64 d d))) (.f64 M (.f64 M h))))
	47.8b	(.f64 1/4 (exp.f64 (.f64 2 (log.f64 (.f64 (/.f64 D d) (.f64 M (sqrt.f64 h)))))))
	40.6b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	40.6b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2)) 3))
	28.5b	(.f64 1/4 (/.f64 (.f64 (/.f64 D d) (.f64 h (.f64 M M))) (/.f64 d D)))
	61.8b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) 3/2))))

Compiler

Compiled 2803 to 1446 computations (48.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (/.f64 D d) 2)
✓	0.6b	(expm1.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2)))
✓	1.5b	(log1p.f64 (pow.f64 (/.f64 D d) 2))
✓	14.7b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))) (.f64 M (*.f64 M h)))

series158.0ms (1%)

Counts

4 → 120

Calls

30 calls:

16.0ms	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))) (.f64 M (*.f64 M h)))	D	0
14.0ms	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))) (.f64 M (*.f64 M h)))	h	-inf
11.0ms	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))) (.f64 M (*.f64 M h)))	M	inf
10.0ms	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))) (.f64 M (*.f64 M h)))	h	0
9.0ms	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))) (.f64 M (*.f64 M h)))	D	-inf

rewrite64.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`log-prod_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
198×	`log-pow_binary64`
132×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	249	38
2	3051	38

Stop Event

1×	node limit

Counts

4 → 132

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-neg_binary64`
310×	`sub-neg_binary64`
213×	`fma-def_binary64`
206×	`times-frac_binary64`
198×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	2209
1	227	2153
2	698	2099
3	3111	2097

Stop Event

1×	node limit

Counts

252 → 119

prune186.0ms (1.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	2	21	23
Picked	1	0	1
Done	0	0	0
Total	117	26	143

Error

12.2b

Counts

143 → 26

Alt Table

Status	Error	Program
	26.3b	(.f64 1/4 (.f64 (expm1.f64 (exp.f64 (log.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (.f64 M h))))
	32.6b	(.f64 1/4 (.f64 (/.f64 (.f64 M M) (/.f64 d (.f64 D D))) (/.f64 h d)))
	57.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	33.1b	(.f64 1/4 (.f64 (/.f64 1 (/.f64 (.f64 d d) (.f64 D D))) (.f64 M (.f64 M h))))
	29.9b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	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)))))
	50.4b	(log.f64 (pow.f64 (exp.f64 (/.f64 c0 (.f64 w 2))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (*.f64 M M))))))
	26.1b	(.f64 1/4 (.f64 (/.f64 1 (.f64 (/.f64 d D) (/.f64 d D))) (.f64 M (*.f64 M h))))
	61.0b	(.f64 (/.f64 (.f64 c0 c0) (.f64 D D)) (/.f64 (.f64 d d) (.f64 w (.f64 w h))))
	61.3b	(/.f64 (.f64 c0 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M))))) (.f64 w 2))
	27.4b	(.f64 1/4 (.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (*.f64 M h))))
	60.9b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	59.7b	(fma.f64 (.f64 (/.f64 d D) (/.f64 d D)) (.f64 (/.f64 c0 h) (/.f64 c0 (.f64 w w))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h))) -1/4))
	33.1b	(.f64 1/4 (.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (/.f64 D d) 2) 1)) (cbrt.f64 (+.f64 (pow.f64 (/.f64 D d) 2) 1))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 D d) 2) 1)) -1) (.f64 M (*.f64 M h))))
	32.3b	(.f64 1/4 (.f64 (pow.f64 (pow.f64 (pow.f64 (/.f64 D d) 2) 3) 1/3) (.f64 M (.f64 M h))))
	43.9b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (pow.f64 (.f64 M (sqrt.f64 h)) 2)))
	45.8b	(.f64 1/4 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2) 3)))
	27.2b	(.f64 1/4 (.f64 (/.f64 (/.f64 (.f64 D (/.f64 D d)) (pow.f64 (cbrt.f64 d) 2)) (cbrt.f64 d)) (.f64 M (*.f64 M h))))
	31.1b	(.f64 1/4 (/.f64 (.f64 (.f64 D (/.f64 D d)) (.f64 h (*.f64 M M))) d))
	39.9b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 (/.f64 D d)) (.f64 (sqrt.f64 (/.f64 D d)) (/.f64 D d))) (.f64 M (.f64 M h))))
	28.5b	(.f64 1/4 (/.f64 (.f64 (/.f64 D d) (.f64 h (.f64 M M))) (/.f64 d D)))
▶	25.9b	(.f64 1/4 (.f64 (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (.f64 M h))))
	47.8b	(.f64 1/4 (exp.f64 (.f64 2 (log.f64 (.f64 (/.f64 D d) (.f64 M (sqrt.f64 h)))))))
	40.6b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	40.6b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2)) 3))
	61.8b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) 3/2))))

Compiler

Compiled 4000 to 2301 computations (42.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (/.f64 D d) 2)
✓	0.6b	(expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2)))))
	1.5b	(log1p.f64 (pow.f64 (/.f64 D d) 2))
✓	14.7b	(.f64 (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (*.f64 M h)))

series153.0ms (1%)

Counts

2 → 72

Calls

18 calls:

50.0ms	(.f64 (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (*.f64 M h)))	d	inf
11.0ms	(.f64 (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (*.f64 M h)))	h	inf
10.0ms	(.f64 (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (*.f64 M h)))	h	0
10.0ms	(.f64 (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (*.f64 M h)))	h	-inf
10.0ms	(.f64 (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (*.f64 M h)))	D	inf

rewrite49.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`log-prod_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
213×	`log-pow_binary64`
144×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	291	22
2	3278	22

Stop Event

1×	node limit

Counts

2 → 66

simplify115.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
444×	`associate-/l*_binary64`
295×	`associate-l_binary64`
293×	`unswap-sqr_binary64`
236×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	1152
1	37	1152
2	105	1152
3	464	1152
4	3703	1152
5	4269	1152
6	4363	1152
7	4510	1152
8	4674	1152
9	4852	1152

Stop Event

1×	node limit

Counts

138 → 71

prune180.0ms (1.2%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	25	25
Picked	0	1	1
Done	0	0	0
Total	121	26	147

Error

12.2b

Counts

147 → 26

Alt Table

Status	Error	Program
	26.3b	(.f64 1/4 (.f64 (expm1.f64 (exp.f64 (log.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (.f64 M h))))
	32.6b	(.f64 1/4 (.f64 (/.f64 (.f64 M M) (/.f64 d (.f64 D D))) (/.f64 h d)))
	57.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	33.1b	(.f64 1/4 (.f64 (/.f64 1 (/.f64 (.f64 d d) (.f64 D D))) (.f64 M (.f64 M h))))
	29.9b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	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)))))
	50.4b	(log.f64 (pow.f64 (exp.f64 (/.f64 c0 (.f64 w 2))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (*.f64 M M))))))
	26.1b	(.f64 1/4 (.f64 (/.f64 1 (.f64 (/.f64 d D) (/.f64 d D))) (.f64 M (*.f64 M h))))
	61.0b	(.f64 (/.f64 (.f64 c0 c0) (.f64 D D)) (/.f64 (.f64 d d) (.f64 w (.f64 w h))))
	61.3b	(/.f64 (.f64 c0 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M))))) (.f64 w 2))
	27.4b	(.f64 1/4 (.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (*.f64 M h))))
	60.9b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	59.7b	(fma.f64 (.f64 (/.f64 d D) (/.f64 d D)) (.f64 (/.f64 c0 h) (/.f64 c0 (.f64 w w))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h))) -1/4))
	33.1b	(.f64 1/4 (.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (/.f64 D d) 2) 1)) (cbrt.f64 (+.f64 (pow.f64 (/.f64 D d) 2) 1))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 D d) 2) 1)) -1) (.f64 M (*.f64 M h))))
	32.3b	(.f64 1/4 (.f64 (pow.f64 (pow.f64 (pow.f64 (/.f64 D d) 2) 3) 1/3) (.f64 M (.f64 M h))))
	43.9b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (pow.f64 (.f64 M (sqrt.f64 h)) 2)))
	45.8b	(.f64 1/4 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2) 3)))
	27.2b	(.f64 1/4 (.f64 (/.f64 (/.f64 (.f64 D (/.f64 D d)) (pow.f64 (cbrt.f64 d) 2)) (cbrt.f64 d)) (.f64 M (*.f64 M h))))
	31.1b	(.f64 1/4 (/.f64 (.f64 (.f64 D (/.f64 D d)) (.f64 h (*.f64 M M))) d))
	39.9b	(.f64 1/4 (.f64 (.f64 (sqrt.f64 (/.f64 D d)) (.f64 (sqrt.f64 (/.f64 D d)) (/.f64 D d))) (.f64 M (.f64 M h))))
	28.5b	(.f64 1/4 (/.f64 (.f64 (/.f64 D d) (.f64 h (.f64 M M))) (/.f64 d D)))
✓	25.9b	(.f64 1/4 (.f64 (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (/.f64 D d) 2))))) (.f64 M (.f64 M h))))
	47.8b	(.f64 1/4 (exp.f64 (.f64 2 (log.f64 (.f64 (/.f64 D d) (.f64 M (sqrt.f64 h)))))))
	40.6b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	40.6b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2)) 3))
	61.8b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) 3/2))))

Compiler

Compiled 3435 to 1954 computations (43.1% saved)

regimes1.1s (7.2%)

Accuracy

Total 10.5b remaining (49.7%)

Threshold costs 0b (0%)

Counts

65 → 2

Compiler

Compiled 21171 to 13021 computations (38.5% saved)

bsearch36.0ms (0.2%)

Algorithm

1×	binary-search

Calls

1 calls:

31.0ms

Steps

Iters	Point		Range
1.6452659381703685e-298	∈ [	2.193308326067954e-300	,	7.414742103011921e-293	]

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	43
1	29	43

Stop Event

1×

saturated

end324.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 765 to 507 computations (33.7% saved)

Details

analyze2.5s (16.2%)

sample8.5s (55.1%)

preprocess47.0ms (0.3%)

simplify30.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series858.0ms (5.5%)

rewrite54.0ms (0.3%)

simplify171.0ms (1.1%)

prune355.0ms (2.3%)

localize8.0ms (0.1%)

series129.0ms (0.8%)

rewrite50.0ms (0.3%)

simplify107.0ms (0.7%)

prune138.0ms (0.9%)

localize10.0ms (0.1%)

series158.0ms (1%)

rewrite64.0ms (0.4%)

simplify62.0ms (0.4%)

prune186.0ms (1.2%)

localize15.0ms (0.1%)

series153.0ms (1%)

rewrite49.0ms (0.3%)

simplify115.0ms (0.7%)

prune180.0ms (1.2%)

regimes1.1s (7.2%)

bsearch36.0ms (0.2%)

simplify2.0ms (0%)

end324.0ms (2.1%)

Profiling