Details

analyze662.0ms (10.3%)

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
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
32.8%	67.1%	0.1%	9
43.7%	43.7%	12.6%	10
46.8%	40.6%	12.6%	11
52.7%	34.7%	12.6%	12
58.5%	22.6%	18.9%	13
60.5%	20.7%	18.9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample33.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify13.0ms (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`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	8
2	16	8
3	17	8
4	17	8

prune10.0ms (0.2%)

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

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 34 to 17 computations (50% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (*.f64 y z) x)

series17.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

17.0ms

(fma.f64 z (*.f64 y z) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 z (*.f64 y z) x)

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

557×	`fma-def_binary64`
534×	`unswap-sqr_binary64`
444×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	382
1	32	365
2	56	365
3	152	365
4	615	365
5	2186	365
6	2764	365
7	4969	365
8	5049	365

prune30.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	4	24

Error

0.0b

Counts

24 → 4

Alt Table

Status	Error	Program
	40.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (.f64 y z) x) (fma.f64 z (.f64 y z) x)) (fma.f64 z (*.f64 y z) x)))
▶	5.7b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
✓	0.1b	(fma.f64 z (*.f64 y z) x)
	32.1b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))

Compiler

Compiled 340 to 103 computations (69.7% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.8b	(*.f64 y (pow.f64 z 2))

series15.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

15.0ms

(*.f64 y (pow.f64 z 2))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

8.0ms

(*.f64 y (pow.f64 z 2))

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

925×	`unswap-sqr_binary64`
454×	`sqr-pow_binary64`
431×	`log-prod_binary64`
409×	`times-frac_binary64`
361×	`*-commutative_binary64`

Counts

29 → 45

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	327
1	99	249
2	264	239
3	777	239
4	1259	239
5	3462	239
6	3911	239
7	4904	239
8	4921	239

prune64.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	40	5	45
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	41	8	49

Error

0.0b

Counts

49 → 8

Alt Table

Status	Error	Program
✓	5.7b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
	32.5b	(+.f64 (.f64 (.f64 z (sqrt.f64 y)) (*.f64 z (sqrt.f64 y))) x)
	32.1b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
	5.9b	(+.f64 (.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (cbrt.f64 (pow.f64 z 2))) x)
	6.1b	(+.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (pow.f64 z 2)) (cbrt.f64 (pow.f64 z 2)))) (cbrt.f64 (pow.f64 z 2))) x)
▶	2.0b	(+.f64 (.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2)) x)
	35.4b	(+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (pow.f64 z 2))) x)
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 771 to 424 computations (45% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.7b	(cbrt.f64 z)
✓	6.1b	(.f64 y (.f64 z (cbrt.f64 z)))

series876.0ms (13.6%)

Counts

4 → 72

Calls

4 calls:

703.0ms	(.f64 y (.f64 z (cbrt.f64 z)))
76.0ms	(pow.f64 (cbrt.f64 z) 2)
53.0ms	(cbrt.f64 z)
43.0ms	(.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
21×	`prod-exp_binary64`
16×	`add-cbrt-cube_binary64`
12×	`unpow-prod-down_binary64`
12×	`associate-r_binary64`

Counts

4 → 91

Calls

4 calls:

18.0ms	(.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2))
7.0ms	(.f64 y (.f64 z (cbrt.f64 z)))
3.0ms	(pow.f64 (cbrt.f64 z) 2)
1.0ms	(cbrt.f64 z)

simplify350.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

526×	`*-commutative_binary64`
370×	`log-prod_binary64`
356×	`sqr-pow_binary64`
285×	`pow-sqr_binary64`
273×	`exp-prod_binary64`

Counts

163 → 133

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	125	1563
1	277	1354
2	949	1266
3	1716	1266
4	3618	1212
5	4348	1202
6	4985	1202
7	4807	1202

prune263.0ms (4.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	150	9	159

Error

0.0b

Counts

159 → 9

Alt Table

Status	Error	Program
✓	5.7b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
	32.5b	(+.f64 (.f64 (.f64 z (sqrt.f64 y)) (*.f64 z (sqrt.f64 y))) x)
	32.1b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
	5.9b	(+.f64 (.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (cbrt.f64 (pow.f64 z 2))) x)
	6.1b	(+.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (pow.f64 z 2)) (cbrt.f64 (pow.f64 z 2)))) (cbrt.f64 (pow.f64 z 2))) x)
✓	2.0b	(+.f64 (.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2)) x)
	35.4b	(+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (pow.f64 z 2))) x)
▶	2.1b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (*.f64 z (cbrt.f64 z)))) (pow.f64 (cbrt.f64 z) 2)) x)
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 2867 to 1250 computations (56.4% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 y)
	0.7b	(cbrt.f64 z)
✓	1.5b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z (cbrt.f64 z))))
✓	4.6b	(.f64 (cbrt.f64 y) (.f64 z (cbrt.f64 z)))

series1.6s (24.6%)

Counts

3 → 60

Calls

3 calls:

861.0ms	(.f64 (cbrt.f64 y) (.f64 z (cbrt.f64 z)))
671.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z (cbrt.f64 z))))
57.0ms	(cbrt.f64 y)

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64`
29×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

3 → 66

Calls

3 calls:

19.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z (cbrt.f64 z))))
10.0ms	(.f64 (cbrt.f64 y) (.f64 z (cbrt.f64 z)))
1.0ms	(cbrt.f64 y)

simplify171.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

567×	`unswap-sqr_binary64`
420×	`*-commutative_binary64`
344×	`fma-def_binary64`
297×	`exp-prod_binary64`
238×	`fma-neg_binary64`

Counts

126 → 99

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1634
1	281	1418
2	904	1239
3	1917	1170
4	4531	1092
5	4895	1092

prune290.0ms (4.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	171	9	180

Error

0.0b

Counts

180 → 9

Alt Table

Status	Error	Program
✓	5.7b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
	32.5b	(+.f64 (.f64 (.f64 z (sqrt.f64 y)) (*.f64 z (sqrt.f64 y))) x)
	32.1b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
	5.9b	(+.f64 (.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (cbrt.f64 (pow.f64 z 2))) x)
	6.1b	(+.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (pow.f64 z 2)) (cbrt.f64 (pow.f64 z 2)))) (cbrt.f64 (pow.f64 z 2))) x)
✓	2.0b	(+.f64 (.f64 (.f64 y (*.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2)) x)
	35.4b	(+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (pow.f64 z 2))) x)
✓	2.1b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (*.f64 z (cbrt.f64 z)))) (pow.f64 (cbrt.f64 z) 2)) x)
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 4269 to 1513 computations (64.6% saved)

regimes284.0ms (4.4%)

Accuracy

Total 0.1b remaining (74.6%)

Threshold costs 0.1b (74.6%)

Counts

17 → 1

Compiler

Compiled 1250 to 740 computations (40.8% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	10	10

end1.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

sample1.4s (21.5%)

Algorithm

1×

intervals

Results

633.0ms	8000×	body	128	valid
37.0ms	615×	body	128	invalid

Compiler

Compiled 165 to 101 computations (38.8% saved)

Details

analyze662.0ms (10.3%)

sample33.0ms (0.5%)

simplify13.0ms (0.2%)

prune10.0ms (0.2%)

localize9.0ms (0.1%)

series17.0ms (0.3%)

rewrite1.0ms (0%)

simplify116.0ms (1.8%)

prune30.0ms (0.5%)

localize10.0ms (0.1%)

series15.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify119.0ms (1.8%)

prune64.0ms (1%)

localize16.0ms (0.2%)

series876.0ms (13.6%)

rewrite38.0ms (0.6%)

simplify350.0ms (5.4%)

prune263.0ms (4.1%)

localize25.0ms (0.4%)

series1.6s (24.6%)

rewrite44.0ms (0.7%)

simplify171.0ms (2.6%)

prune290.0ms (4.5%)

regimes284.0ms (4.4%)

simplify9.0ms (0.1%)

end1.0ms (0%)

sample1.4s (21.5%)

Profiling