Details

analyze2.8s (23.9%)

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%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample2.2s (18.9%)

Results

1.5s	8256×	body	128	valid
734.0ms	4053×	body	128	invalid

Compiler

Compiled 50 to 36 computations (28% saved)

preprocess28.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

19×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	506
1	146	506
0	7	7

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	19	23

Stop Event

1×

saturated

Counts

1 → 2

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)) c)

Compiler

Compiled 86 to 56 computations (34.9% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)) c)
✓	0.0b	(-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))

series59.0ms (0.5%)

Counts

2 → 156

Calls

39 calls:

3.0ms	(+.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)) c)	c	-inf
2.0ms	(+.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)) c)	b	-inf
2.0ms	(+.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)) c)	c	inf
2.0ms	(+.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)) c)	y	0
2.0ms	(-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))	t	0

rewrite56.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

314×	`expm1-udef_binary64`
314×	`log1p-udef_binary64`
309×	`log-pow_binary64`
172×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	43
1	327	43
2	3491	43

Stop Event

1×	node limit

Counts

2 → 50

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`fma-def_binary64`
2×	`fma-neg_binary64`
2×	`fma-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	2869
1	35	2869
2	37	2869

Stop Event

1×

saturated

Counts

206 → 69

prune81.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Error

Counts

70 → 4

Alt Table

Status	Error	Program
	1.2b	(.f64 (cbrt.f64 (+.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)) c)) (pow.f64 (cbrt.f64 (+.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)) 2))
	23.2b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4))) c)
	32.0b	(+.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) 2))) c)
▶	0.0b	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))

Compiler

Compiled 1797 to 950 computations (47.1% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))
✓	0.0b	(+.f64 c (.f64 1/16 (.f64 t z)))

series49.0ms (0.4%)

Counts

2 → 93

Calls

30 calls:

4.0ms	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))	b	inf
4.0ms	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))	t	-inf
3.0ms	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))	z	0
3.0ms	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))	y	inf
2.0ms	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))	z	inf

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

314×	`expm1-udef_binary64`
314×	`log1p-udef_binary64`
311×	`log-pow_binary64`
172×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	33
1	327	33
2	3500	33

Stop Event

1×	node limit

Counts

2 → 51

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	1680
1	29	1680

Stop Event

1×

saturated

Counts

144 → 65

prune70.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Error

Counts

69 → 4

Alt Table

Status	Error	Program
	23.2b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4))) c)
	32.0b	(+.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) 2))) c)
✓	0.0b	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))
▶	1.0b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))

Compiler

Compiled 1689 to 896 computations (47% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 c (.f64 1/16 (.f64 t z)))
✓	0.2b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2)
✓	0.5b	(cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))))

series1.5s (12.7%)

Counts

3 → 94

Calls

51 calls:

500.0ms	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))	c	0
407.0ms	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))	x	0
95.0ms	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))	b	inf
50.0ms	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))	a	-inf
48.0ms	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))	a	0

rewrite60.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

362×	`expm1-udef_binary64`
362×	`log1p-udef_binary64`
203×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	60
1	398	60
2	4070	60

Stop Event

1×	node limit

Counts

3 → 47

simplify1.1s (8.9%)

Algorithm

1×	egg-herbie

Rules

1748×	`sqr-pow_binary64`
405×	`pow-sqr_binary64`
85×	`cube-prod_binary64`
85×	`cube-mult_binary64`
85×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	329	8258
1	573	8258
2	726	8258
3	897	8258
4	1089	8258
5	1279	8258
6	1485	8258
7	1699	8258
8	1929	8258
9	2169	8258
10	2425	8258
11	2690	8258
12	2710	8258
13	2720	8258
14	2720	8258
15	2996	8258
16	3276	8258
17	3582	8258
18	3897	8258
19	4228	8258
20	4568	8258
21	4636	8258
22	4686	8258
23	4686	8258
24	4985	8258

Stop Event

1×	node limit

Counts

141 → 121

prune388.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	214	4	218

Error

Counts

218 → 4

Alt Table

Status	Error	Program
▶	23.2b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4))) c)
	32.0b	(+.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) 2))) c)
✓	0.0b	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))
✓	1.0b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))

Compiler

Compiled 13263 to 7287 computations (45.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4)))
✓	0.2b	(pow.f64 (fma.f64 x y (/.f64 (*.f64 z t) 16)) 2)
✓	1.2b	(cbrt.f64 (fma.f64 x y (/.f64 (*.f64 z t) 16)))
✓	26.6b	(cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (*.f64 z t) 16)) 2))

series610.0ms (5.1%)

Counts

4 → 128

Calls

54 calls:

61.0ms	(fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4)))	y	0
60.0ms	(fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4)))	a	0
51.0ms	(fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4)))	x	0
49.0ms	(fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4)))	b	0
45.0ms	(fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4)))	b	-inf

rewrite66.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

334×	`log-pow_binary64`
323×	`expm1-udef_binary64`
323×	`log1p-udef_binary64`
182×	`add-sqr-sqrt_binary64`
174×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	83
1	367	65
2	3624	65

Stop Event

1×	node limit

Counts

4 → 77

simplify1.1s (9.1%)

Algorithm

1×	egg-herbie

Rules

1767×	`sqr-pow_binary64`
360×	`pow-sqr_binary64`
81×	`fma-def_binary64`
72×	`cube-mult_binary64`
72×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	406	8670
1	686	8670
2	844	8670
3	1006	8670
4	1190	8670
5	1377	8670
6	1576	8670
7	1782	8670
8	2000	8670
9	2226	8670
10	2465	8670
11	2712	8670
12	2758	8670
13	2786	8670
14	2808	8670
15	2808	8670
16	3031	8670
17	3261	8670
18	3543	8670
19	3831	8670
20	4126	8670
21	4434	8670
22	4749	8670
23	4807	8670
24	4847	8670
25	4881	8670
26	4881	8670

Stop Event

1×	node limit

Counts

205 → 151

prune277.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	151	4	155

Error

Counts

155 → 4

Alt Table

Status	Error	Program
✓	23.2b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) 2)) (cbrt.f64 (fma.f64 x y (/.f64 (.f64 z t) 16))) (neg.f64 (/.f64 (*.f64 a b) 4))) c)
	32.0b	(+.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) 2))) c)
✓	0.0b	(-.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z)))) (.f64 1/4 (.f64 a b)))
✓	1.0b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) 2) (cbrt.f64 (fma.f64 y x (+.f64 c (.f64 1/16 (.f64 t z))))) (neg.f64 (.f64 1/4 (.f64 a b))))

Compiler

Compiled 9820 to 6412 computations (34.7% saved)

regimes1.1s (9.1%)

Accuracy

Total 0.0b remaining (2.4%)

Threshold costs 0.0b (2.4%)

Counts

46 → 1

Compiler

Compiled 19738 to 13892 computations (29.6% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23

Stop Event

1×

saturated

end119.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 185 to 124 computations (33% saved)

Details

analyze2.8s (23.9%)

sample2.2s (18.9%)

preprocess28.0ms (0.2%)

simplify6.0ms (0.1%)

prune6.0ms (0.1%)

localize18.0ms (0.2%)

series59.0ms (0.5%)

rewrite56.0ms (0.5%)

simplify46.0ms (0.4%)

prune81.0ms (0.7%)

localize11.0ms (0.1%)

series49.0ms (0.4%)

rewrite51.0ms (0.4%)

simplify22.0ms (0.2%)

prune70.0ms (0.6%)

localize16.0ms (0.1%)

series1.5s (12.7%)

rewrite60.0ms (0.5%)

simplify1.1s (8.9%)

prune388.0ms (3.3%)

localize17.0ms (0.1%)

series610.0ms (5.1%)

rewrite66.0ms (0.6%)

simplify1.1s (9.1%)

prune277.0ms (2.3%)

regimes1.1s (9.1%)

simplify1.0ms (0%)

end119.0ms (1%)

Profiling