Details

analyze2.8s (17%)

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 (55.1%)

Results

3.2s	16205×	body	128	invalid
2.1s	2194×	body	4096	valid
1.4s	1223×	body	8192	valid
1.1s	1356×	body	2048	valid
490.0ms	2486×	body	128	valid
408.0ms	596×	body	1024	valid
133.0ms	261×	body	512	valid
48.0ms	140×	body	256	valid
44.0ms	56×	body	2048	invalid
33.0ms	56×	body	1024	invalid
18.0ms	41×	body	512	invalid
11.0ms	12×	body	4096	invalid
7.0ms	21×	body	256	invalid
5.0ms	5×	body	8192	exit

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)

simplify32.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

60.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	60.3b	(.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)))))
	62.1b	(.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)))))

Status

Error

Program

▶

60.3b

(*.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)))))

62.1b

(*.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)))))

Compiler

Compiled 321 to 134 computations (58.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.8b	(.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)))))
✓	14.8b	(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)))
✓	18.3b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	26.5b	(+.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))))

series843.0ms (5.2%)

Counts

4 → 276

Calls

69 calls:

34.0ms	(.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
28.0ms	(.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
23.0ms	(+.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

rewrite49.0ms (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

simplify210.0ms (1.3%)

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

prune340.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	235	13	248
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	237	13	250

Error

16.5b

Counts

250 → 13

Alt Table

Status	Error	Program
▶	27.2b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (*.f64 M h))))
	53.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	36.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	40.6b	(.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))))
	61.0b	(/.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))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 -1 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (*.f64 w h))))))
	56.1b	(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))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 h (.f64 w (*.f64 M M))) c0)) -1/2)))
	59.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	49.9b	(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))))))
	60.6b	(.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 1 (.f64 w (.f64 h (.f64 D D)))))) (.f64 M M)))))
	61.9b	(.f64 (/.f64 c0 (.f64 2 w)) (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 3) (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) 3/2)) (+.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (-.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) (.f64 (.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))))))))
	50.9b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))

Compiler

Compiled 14683 to 6155 computations (58.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 M (.f64 M h))
✓	0.2b	(*.f64 (/.f64 D d) (/.f64 D d))
✓	11.3b	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))

series139.0ms (0.9%)

Counts

3 → 96

Calls

24 calls:

12.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))	D	inf
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	inf
10.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))	d	-inf
10.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))	M	inf

rewrite52.0ms (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

simplify118.0ms (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

prune119.0ms (0.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	85	18	103

Error

11.4b

Counts

103 → 18

Alt Table

Status	Error	Program
✓	27.2b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (*.f64 M h))))
	31.2b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	49.9b	(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))))))
	42.5b	(.f64 1/4 (.f64 (exp.f64 (.f64 2 (log.f64 (/.f64 D d)))) (.f64 M (*.f64 M h))))
	61.0b	(/.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))
	42.8b	(.f64 1/4 (expm1.f64 (log1p.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))))
	60.6b	(.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 1 (.f64 w (.f64 h (.f64 D D)))))) (.f64 M M)))))
	42.8b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2)) 3))
	61.9b	(.f64 (/.f64 c0 (.f64 2 w)) (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 3) (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) 3/2)) (+.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (-.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) (.f64 (.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))))))))
	30.7b	(.f64 1/4 (/.f64 (.f64 D (.f64 (/.f64 D d) (.f64 h (*.f64 M M)))) d))
	56.1b	(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))
	31.7b	(.f64 1/4 (.f64 (.f64 D (/.f64 D (.f64 d d))) (.f64 M (.f64 M h))))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 h (.f64 w (*.f64 M M))) c0)) -1/2)))
	59.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	30.9b	(.f64 1/4 (.f64 (sqrt.f64 (pow.f64 (/.f64 D d) 4)) (.f64 M (.f64 M h))))
▶	27.9b	(.f64 1/4 (.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (*.f64 M h))))
	42.7b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	29.3b	(.f64 1/4 (/.f64 (.f64 (/.f64 D d) (.f64 h (.f64 M M))) (/.f64 d D)))

Compiler

Compiled 2752 to 1285 computations (53.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 M (.f64 M h))
✓	0.1b	(*.f64 (/.f64 d D) d)
✓	3.3b	(/.f64 D (*.f64 (/.f64 d D) d))
✓	11.3b	(.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (.f64 M h)))

series147.0ms (0.9%)

Counts

3 → 96

Calls

24 calls:

16.0ms	(.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (.f64 M h)))	h	0
12.0ms	(.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (.f64 M h)))	D	inf
12.0ms	(.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (.f64 M h)))	h	-inf
11.0ms	(.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (.f64 M h)))	M	inf
9.0ms	(.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (.f64 M h)))	h	inf

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log-prod_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
199×	`log-pow_binary64`
155×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	235	29
2	3386	29

Stop Event

1×	node limit

Counts

3 → 102

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

642×	`times-frac_binary64`
448×	`associate-/l*_binary64`
301×	`unswap-sqr_binary64`
290×	`associate-l_binary64`
240×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	1320
1	38	1320
2	106	1320
3	467	1320
4	3739	1320
5	4321	1320
6	4415	1320
7	4562	1320
8	4726	1320
9	4904	1320

Stop Event

1×	node limit

Counts

198 → 108

prune189.0ms (1.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	3	13	16
Picked	1	0	1
Done	0	1	1
Total	130	17	147

Error

11.4b

Counts

147 → 17

Alt Table

Status	Error	Program
	31.7b	(.f64 1/4 (.f64 (.f64 D (/.f64 D (.f64 d d))) (.f64 M (.f64 M h))))
▶	27.8b	(.f64 1/4 (/.f64 (/.f64 (.f64 D (.f64 M (.f64 M h))) (/.f64 d D)) d))
✓	27.2b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (*.f64 M h))))
	31.2b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	28.7b	(.f64 1/4 (/.f64 D (/.f64 (.f64 d (/.f64 d D)) (.f64 M (.f64 M h)))))
	61.0b	(/.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))
	42.8b	(.f64 1/4 (expm1.f64 (log1p.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))))
	60.6b	(.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 1 (.f64 w (.f64 h (.f64 D D)))))) (.f64 M M)))))
	42.8b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2)) 3))
	61.9b	(.f64 (/.f64 c0 (.f64 2 w)) (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 3) (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) 3/2)) (+.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (-.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) (.f64 (.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))))))))
	30.7b	(.f64 1/4 (/.f64 (.f64 D (.f64 (/.f64 D d) (.f64 h (*.f64 M M)))) d))
	56.1b	(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))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 h (.f64 w (*.f64 M M))) c0)) -1/2)))
	59.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	42.5b	(.f64 1/4 (.f64 (exp.f64 (.f64 2 (log.f64 (/.f64 D d)))) (.f64 M (*.f64 M h))))
	32.1b	(.f64 1/4 (.f64 (.f64 M M) (.f64 (/.f64 (/.f64 D d) d) (*.f64 D h))))
	29.3b	(.f64 1/4 (/.f64 (.f64 (/.f64 D d) (.f64 h (.f64 M M))) (/.f64 d D)))

Compiler

Compiled 3463 to 1529 computations (55.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 M (.f64 M h))
✓	4.3b	(.f64 D (.f64 M (*.f64 M h)))
✓	4.7b	(/.f64 (/.f64 (.f64 D (.f64 M (*.f64 M h))) (/.f64 d D)) d)
✓	5.5b	(/.f64 (.f64 D (.f64 M (*.f64 M h))) (/.f64 d D))

series169.0ms (1%)

Counts

3 → 132

Calls

33 calls:

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

rewrite71.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
207×	`log-pow_binary64`
138×	`times-frac_binary64`
130×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	242	42
2	3826	42

Stop Event

1×	node limit

Counts

3 → 121

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

711×	`times-frac_binary64`
488×	`associate-/l*_binary64`
333×	`associate-l_binary64`
322×	`unswap-sqr_binary64`
278×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	2040
1	48	2040
2	125	2040
3	515	2040
4	4174	2040
5	4782	2040
6	4869	2040
7	4999	2040

Stop Event

1×	node limit

Counts

253 → 130

prune218.0ms (1.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	4	11	15
Picked	1	0	1
Done	1	0	1
Total	149	19	168

Error

11.1b

Counts

168 → 19

Alt Table

Status	Error	Program
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 h (.f64 w (*.f64 M M))) c0)) -1/2)))
	24.3b	(.f64 1/4 (/.f64 (.f64 (.f64 D M) (.f64 (*.f64 M h) (/.f64 D d))) d))
	35.8b	(.f64 1/4 (/.f64 (/.f64 (log.f64 (pow.f64 (exp.f64 D) (.f64 h (*.f64 M M)))) (/.f64 d D)) d))
	31.2b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	28.7b	(.f64 1/4 (/.f64 D (/.f64 (.f64 d (/.f64 d D)) (.f64 M (.f64 M h)))))
	59.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	30.7b	(.f64 1/4 (/.f64 (.f64 (.f64 (/.f64 (.f64 h (*.f64 M M)) (/.f64 d D)) (pow.f64 (cbrt.f64 D) 2)) (cbrt.f64 D)) d))
	61.0b	(/.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))
	42.8b	(.f64 1/4 (expm1.f64 (log1p.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))))
	60.6b	(.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 1 (.f64 w (.f64 h (.f64 D D)))))) (.f64 M M)))))
	42.8b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2)) 3))
	61.9b	(.f64 (/.f64 c0 (.f64 2 w)) (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 3) (pow.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) 3/2)) (+.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (-.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M)) (.f64 (.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))))))))
	30.3b	(.f64 1/4 (/.f64 (/.f64 (.f64 h (.f64 D (.f64 M M))) (/.f64 d D)) d))
	29.2b	(.f64 1/4 (/.f64 (.f64 (.f64 D D) (.f64 (/.f64 M d) (*.f64 M h))) d))
	56.1b	(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))
	35.8b	(.f64 1/4 (/.f64 (exp.f64 (log.f64 (.f64 D (/.f64 (.f64 h (.f64 M M)) (/.f64 d D))))) d))
	32.6b	(.f64 1/4 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 D (.f64 h (.f64 M M))))) (/.f64 d D)) d))
	24.4b	(.f64 1/4 (/.f64 (.f64 (/.f64 (.f64 D M) d) (/.f64 (.f64 M h) (/.f64 1 D))) d))
	29.3b	(.f64 1/4 (/.f64 (.f64 (/.f64 D d) (.f64 h (.f64 M M))) (/.f64 d D)))

Compiler

Compiled 3592 to 1431 computations (60.2% saved)

regimes1.1s (6.6%)

Accuracy

Total 10.2b remaining (50.8%)

Threshold costs 0b (0%)

Counts

68 → 2

Compiler

Compiled 21157 to 13142 computations (37.9% saved)

bsearch151.0ms (0.9%)

Algorithm

1×	binary-search

Calls

1 calls:

148.0ms

Steps

Iters	Point		Range
4.0293615430633335e-307	∈ [	9.61302668559806e-309	,	6.75437064033358e-303	]

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	49
1	35	49

Stop Event

1×

saturated

end251.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 700 to 405 computations (42.1% saved)

Details

analyze2.8s (17%)

sample9.0s (55.1%)

preprocess47.0ms (0.3%)

simplify32.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series843.0ms (5.2%)

rewrite49.0ms (0.3%)

simplify210.0ms (1.3%)

prune340.0ms (2.1%)

localize8.0ms (0.1%)

series139.0ms (0.9%)

rewrite52.0ms (0.3%)

simplify118.0ms (0.7%)

prune119.0ms (0.7%)

localize14.0ms (0.1%)

series147.0ms (0.9%)

rewrite62.0ms (0.4%)

simplify109.0ms (0.7%)

prune189.0ms (1.2%)

localize9.0ms (0.1%)

series169.0ms (1%)

rewrite71.0ms (0.4%)

simplify104.0ms (0.6%)

prune218.0ms (1.3%)

regimes1.1s (6.6%)

bsearch151.0ms (0.9%)

simplify2.0ms (0%)

end251.0ms (1.5%)

Profiling