Details

analyze380.0ms (8.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample2.2s (46%)

Results

1.0s	3929×	body	256	valid
583.0ms	1503×	body	512	valid
407.0ms	2824×	body	128	valid
130.0ms	920×	body	128	invalid

Compiler

Compiled 86 to 62 computations (27.9% saved)

preprocess42.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

801×	`fma-def_binary64`
685×	`div-sub_binary64`
295×	`fma-neg_binary64`
210×	`associate-/l*_binary64`
209×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	104
1	99	88
2	220	88
3	445	88
4	763	88
5	1256	88
6	2230	88
7	4450	88
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 20 to 14 computations (30% saved)

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

763×	`fma-neg_binary64`
619×	`times-frac_binary64`
367×	`fma-def_binary64`
242×	`distribute-rgt-in_binary64`
239×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	72	22
3	163	22
4	267	22
5	436	22
6	747	22
7	1335	22
8	2689	22
9	4086	22

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

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

53.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	53.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
▶	53.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	27.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series127.0ms (2.7%)

Counts

4 → 96

Calls

36 calls:

10.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))	a	inf
10.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))	a	-inf
9.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))	c	inf
8.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))	c	-inf
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))	a	inf

rewrite77.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

278×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	342	62
2	4865	62

Stop Event

1×	node limit

Counts

4 → 158

simplify49.0ms (1%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
432×	`fma-def_binary64`
423×	`associate-/r*_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	402	2164
2	1405	2078

Stop Event

1×	node limit

Counts

254 → 232

prune152.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	228	4	232
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	228	6	234

Error

0.2b

Counts

234 → 6

Alt Table

Status	Error	Program
	53.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	5.9b	(/.f64 (neg.f64 c) b)
	2.0b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
✓	53.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	52.7b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 c (.f64 a -4))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a))
▶	1.7b	(-.f64 (.f64 -2 (/.f64 a (/.f64 (pow.f64 b 5) (.f64 a (pow.f64 c 3))))) (fma.f64 5 (.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4)) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))

Compiler

Compiled 6120 to 3777 computations (38.3% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 a (pow.f64 c 3))
✓	0.3b	(*.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4))
✓	0.4b	(/.f64 (pow.f64 a 3) (pow.f64 b 7))
✓	0.4b	(/.f64 (*.f64 c c) (pow.f64 b 3))

series166.0ms (3.5%)

Counts

4 → 84

Calls

27 calls:

14.0ms	(*.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4))	a	-inf
12.0ms	(*.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4))	a	0
12.0ms	(*.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4))	c	inf
11.0ms	(*.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4))	a	inf
11.0ms	(*.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4))	c	-inf

rewrite62.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

285×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
164×	`log1p-expm1-u_binary64`
164×	`expm1-log1p-u_binary64`
160×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	43
1	369	43
2	4533	43

Stop Event

1×	node limit

Counts

4 → 115

simplify31.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

941×	`times-frac_binary64`
642×	`associate-/l*_binary64`
397×	`associate-l_binary64`
329×	`associate-r_binary64`
311×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	984
1	50	984
2	146	984
3	638	984

Stop Event

1×	node limit

Counts

199 → 121

prune194.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	121	6	127

Error

0.2b

Counts

127 → 6

Alt Table

Status	Error	Program
	53.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	5.9b	(/.f64 (neg.f64 c) b)
▶	2.0b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
✓	53.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	52.7b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 c (.f64 a -4))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a))
✓	1.7b	(-.f64 (.f64 -2 (/.f64 a (/.f64 (pow.f64 b 5) (.f64 a (pow.f64 c 3))))) (fma.f64 5 (.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4)) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))

Compiler

Compiled 5396 to 3444 computations (36.2% saved)

localize32.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.3b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.4b	(*.f64 (pow.f64 c 2) (pow.f64 a 2))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))

series128.0ms (2.7%)

Counts

4 → 0

Calls

27 calls:

12.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))	c	-inf
12.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))	c	0
11.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))	a	inf
11.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))	a	-inf
10.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))	a	0

rewrite61.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`log1p-udef_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
171×	`add-sqr-sqrt_binary64`
169×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	418	34
2	4673	34

Stop Event

1×	node limit

Counts

4 → 92

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

92 → 92

prune181.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	92	6	98

Error

0.2b

Counts

98 → 6

Alt Table

Status	Error	Program
	53.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
▶	2.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (cbrt.f64 (pow.f64 (.f64 c a) 6)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	5.9b	(/.f64 (neg.f64 c) b)
✓	53.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	52.7b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 c (.f64 a -4))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a))
✓	1.7b	(-.f64 (.f64 -2 (/.f64 a (/.f64 (pow.f64 b 5) (.f64 a (pow.f64 c 3))))) (fma.f64 5 (.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4)) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))

Compiler

Compiled 5400 to 3803 computations (29.6% saved)

localize70.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
✓	1.2b	(pow.f64 (*.f64 c a) 6)
✓	2.2b	(cbrt.f64 (pow.f64 (*.f64 c a) 6))

series28.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

4.0ms	(pow.f64 (*.f64 c a) 6)	c	-inf
3.0ms	(pow.f64 (*.f64 c a) 6)	a	-inf
3.0ms	(pow.f64 (*.f64 c a) 6)	c	inf
3.0ms	(pow.f64 (*.f64 c a) 6)	a	inf
3.0ms	(pow.f64 (*.f64 c a) 6)	a	0

rewrite36.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

570×	`log1p-expm1-u_binary64`
570×	`expm1-log1p-u_binary64`
309×	`log-prod_binary64`
170×	`pow2_binary64`
117×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	146	14
2	1669	14

Stop Event

1×	node limit

Counts

2 → 56

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

571×	`sqr-pow_binary64`
510×	`associate-l_binary64`
432×	`associate-r_binary64`
372×	`cube-prod_binary64`
318×	`pow-sqr_binary64`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	11	480
1	27	480
2	71	480
3	292	480
4	1919	480
5	2129	480
6	2486	480
7	2839	480
8	3274	408
9	3809	408
10	4508	336

Stop Event

1×	node limit

Counts

104 → 58

prune185.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	118	6	124

Error

0.2b

Counts

124 → 6

Alt Table

Status	Error	Program
	53.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
✓	2.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (cbrt.f64 (pow.f64 (.f64 c a) 6)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	5.9b	(/.f64 (neg.f64 c) b)
✓	53.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	52.7b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 c (.f64 a -4))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4)))))) (.f64 2 a))
✓	1.7b	(-.f64 (.f64 -2 (/.f64 a (/.f64 (pow.f64 b 5) (.f64 a (pow.f64 c 3))))) (fma.f64 5 (.f64 (/.f64 (pow.f64 a 3) (pow.f64 b 7)) (pow.f64 c 4)) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))

Compiler

Compiled 6792 to 4664 computations (31.3% saved)

regimes220.0ms (4.7%)

Accuracy

Total 1.2b remaining (84.4%)

Threshold costs 0b (0%)

Counts

39 → 1

Compiler

Compiled 6208 to 4502 computations (27.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
22×	`+-commutative_binary64`
19×	`sub-neg_binary64`
19×	`neg-sub0_binary64`
19×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	63
1	45	61
2	64	61
3	91	61
4	121	61
5	154	61
6	176	61
7	189	61
8	193	61

Stop Event

1×

saturated

end151.0ms (3.2%)

Stop Event

1×

fuel

Compiler

Compiled 262 to 187 computations (28.6% saved)

Details

analyze380.0ms (8.1%)

sample2.2s (46%)

preprocess42.0ms (0.9%)

simplify34.0ms (0.7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series127.0ms (2.7%)

rewrite77.0ms (1.6%)

simplify49.0ms (1%)

prune152.0ms (3.2%)

localize25.0ms (0.5%)

series166.0ms (3.5%)

rewrite62.0ms (1.3%)

simplify31.0ms (0.7%)

prune194.0ms (4.1%)

localize32.0ms (0.7%)

series128.0ms (2.7%)

rewrite61.0ms (1.3%)

simplify6.0ms (0.1%)

prune181.0ms (3.9%)

localize70.0ms (1.5%)

series28.0ms (0.6%)

rewrite36.0ms (0.8%)

simplify78.0ms (1.7%)

prune185.0ms (3.9%)

regimes220.0ms (4.7%)

simplify5.0ms (0.1%)

end151.0ms (3.2%)

Profiling