Details

analyze462.0ms (18.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
37.4%	49.9%	12.6%	10
43.7%	43.7%	12.6%	11
49.1%	38.2%	12.6%	12
54.6%	26.5%	18.9%	13
58.5%	22.6%	18.9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample898.0ms (36.3%)

Results

813.0ms	8256×	body	128	valid
70.0ms	660×	body	128	invalid

Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess15.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

16×	`fma-def_binary64`
7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	34	32
2	50	32
3	54	32
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 6 computations (40% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	8
2	16	8
3	17	8

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.7b	(fma.f64 y (*.f64 z z) x)
▶	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y z) z))
✓	0.2b	(.f64 (.f64 y z) z)

series17.0ms (0.7%)

Counts

2 → 60

Calls

15 calls:

2.0ms	(.f64 (.f64 y z) z)	y	-inf
1.0ms	(.f64 (.f64 y z) z)	y	0
1.0ms	(.f64 (.f64 y z) z)	y	inf
1.0ms	(+.f64 x (.f64 (.f64 y z) z))	y	-inf
1.0ms	(+.f64 x (.f64 (.f64 y z) z))	x	-inf

rewrite43.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

929×	`prod-diff_binary64`
762×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
73×	`log1p-expm1-u_binary64`
72×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	149	15
2	2051	15

Stop Event

1×	node limit

Counts

2 → 51

simplify75.0ms (3%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
449×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	423
1	16	423
2	28	423
3	52	423
4	118	423
5	329	423
6	1249	423
7	2149	423
8	2313	423
9	2497	423
10	2705	423
11	2999	423
12	3390	423
13	3870	423
14	4431	423

Stop Event

1×	node limit

Counts

111 → 55

prune31.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

0.0b

Counts

57 → 4

Alt Table

Status	Error	Program
	31.4b	(+.f64 x (pow.f64 (*.f64 (sqrt.f64 y) z) 2))
	5.1b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3))
▶	4.7b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 768 to 256 computations (66.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.5b	(fma.f64 y (*.f64 z z) x)

series15.0ms (0.6%)

Counts

1 → 36

Calls

9 calls:

6.0ms	(fma.f64 y (*.f64 z z) x)	x	-inf
1.0ms	(fma.f64 y (*.f64 z z) x)	y	-inf
1.0ms	(fma.f64 y (*.f64 z z) x)	y	inf
1.0ms	(fma.f64 y (*.f64 z z) x)	y	0
1.0ms	(fma.f64 y (*.f64 z z) x)	x	inf

rewrite32.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

496×	`log1p-expm1-u_binary64`
496×	`expm1-log1p-u_binary64`
311×	`unpow-prod-down_binary64`
265×	`log-prod_binary64`
154×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	118	8
2	1393	8

Stop Event

1×	node limit

Counts

1 → 36

simplify66.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

606×	`sqr-pow_binary64`
441×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
270×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	255
1	16	255
2	28	255
3	52	255
4	115	255
5	338	255
6	1253	255
7	2150	255
8	2314	255
9	2498	255
10	2706	255
11	2998	255
12	3389	255
13	3867	255
14	4430	255

Stop Event

1×	node limit

Counts

72 → 41

prune17.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Error

0.0b

Counts

45 → 4

Alt Table

Status	Error	Program
	31.4b	(+.f64 x (pow.f64 (*.f64 (sqrt.f64 y) z) 2))
▶	5.1b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3))
✓	4.7b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 570 to 197 computations (65.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3))
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3)
✓	8.9b	(.f64 y (.f64 z z))
✓	19.9b	(cbrt.f64 (.f64 y (.f64 z z)))

series99.0ms (4%)

Counts

4 → 60

Calls

27 calls:

30.0ms	(+.f64 x (pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3))	y	-inf
17.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3)	y	-inf
9.0ms	(cbrt.f64 (.f64 y (.f64 z z)))	y	-inf
5.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3)	y	0
5.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3)	z	0

rewrite56.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

912×	`log1p-expm1-u_binary64`
912×	`expm1-log1p-u_binary64`
115×	`egg-rr`
94×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	211	31
2	2556	31

Stop Event

1×	node limit

Counts

4 → 115

simplify80.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
449×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	423
1	16	423
2	28	423
3	52	423
4	118	423
5	329	423
6	1249	423
7	2149	423
8	2313	423
9	2497	423
10	2705	423
11	2999	423
12	3390	423
13	3870	423
14	4431	423

Stop Event

1×	node limit

Counts

175 → 109

prune63.0ms (2.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	108	5	113

Error

0.0b

Counts

113 → 5

Alt Table

Status	Error	Program
	31.4b	(+.f64 x (pow.f64 (*.f64 (sqrt.f64 y) z) 2))
✓	5.1b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3))
▶	4.9b	(+.f64 x (.f64 (.f64 (.f64 y z) (cbrt.f64 (.f64 z z))) (cbrt.f64 z)))
✓	4.7b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 1601 to 594 computations (62.9% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 y z) (cbrt.f64 (*.f64 z z)))
✓	0.3b	(.f64 (.f64 (.f64 y z) (cbrt.f64 (.f64 z z))) (cbrt.f64 z))
✓	0.5b	(cbrt.f64 z)
✓	25.5b	(cbrt.f64 (*.f64 z z))

series163.0ms (6.6%)

Counts

4 → 36

Calls

18 calls:

51.0ms	(.f64 (.f64 (.f64 y z) (cbrt.f64 (.f64 z z))) (cbrt.f64 z))	z	-inf
31.0ms	(.f64 (.f64 y z) (cbrt.f64 (*.f64 z z)))	y	0
29.0ms	(.f64 (.f64 y z) (cbrt.f64 (*.f64 z z)))	y	-inf
24.0ms	(.f64 (.f64 y z) (cbrt.f64 (*.f64 z z)))	y	inf
8.0ms	(cbrt.f64 z)	z	-inf

rewrite49.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

718×	`log1p-expm1-u_binary64`
718×	`expm1-log1p-u_binary64`
145×	`expm1-udef_binary64`
145×	`log1p-udef_binary64`
96×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	178	28
2	2093	28

Stop Event

1×	node limit

Counts

4 → 79

simplify45.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
474×	`unswap-sqr_binary64`
320×	`distribute-lft-neg-in_binary64`
311×	`distribute-rgt-neg-in_binary64`
216×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	304
1	40	304
2	100	304
3	268	304
4	783	304
5	1284	304
6	1942	304
7	3210	304
8	4322	304

Stop Event

1×	node limit

Counts

115 → 85

prune54.0ms (2.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	85	5	90

Error

0.0b

Counts

90 → 5

Alt Table

Status	Error	Program
	31.4b	(+.f64 x (pow.f64 (*.f64 (sqrt.f64 y) z) 2))
✓	5.1b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 y (.f64 z z))) 3))
✓	4.9b	(+.f64 x (.f64 (.f64 (.f64 y z) (cbrt.f64 (.f64 z z))) (cbrt.f64 z)))
✓	4.7b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 1322 to 562 computations (57.5% saved)

regimes69.0ms (2.8%)

Accuracy

Total 0.1b remaining (70.4%)

Threshold costs 0.1b (70.4%)

Counts

12 → 1

Compiler

Compiled 740 to 474 computations (35.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8

Stop Event

1×

saturated

end86.0ms (3.5%)

Stop Event

1×

fuel

Compiler

Compiled 77 to 48 computations (37.7% saved)

Details

analyze462.0ms (18.7%)

sample898.0ms (36.3%)

preprocess15.0ms (0.6%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series17.0ms (0.7%)

rewrite43.0ms (1.7%)

simplify75.0ms (3%)

prune31.0ms (1.3%)

localize4.0ms (0.2%)

series15.0ms (0.6%)

rewrite32.0ms (1.3%)

simplify66.0ms (2.6%)

prune17.0ms (0.7%)

localize10.0ms (0.4%)

series99.0ms (4%)

rewrite56.0ms (2.3%)

simplify80.0ms (3.2%)

prune63.0ms (2.5%)

localize9.0ms (0.4%)

series163.0ms (6.6%)

rewrite49.0ms (2%)

simplify45.0ms (1.8%)

prune54.0ms (2.2%)

regimes69.0ms (2.8%)

simplify2.0ms (0.1%)

end86.0ms (3.5%)

Profiling