Details

analyze1.1s (10.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
13.2%	86.5%	0.2%	11
16.8%	83%	0.2%	12
22.7%	77.1%	0.2%	13
24.1%	74.7%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample130.0ms (1.2%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
4.0ms	97×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	8.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) a)
✓	4.8b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series33.0ms (0.3%)

Counts

2 → 88

Calls

2 calls:

23.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)
10.0ms	(/.f64 (-.f64 z t) a)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(/.f64 (-.f64 z t) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-in_binary64`
686×	`distribute-lft-in_binary64`
589×	`times-frac_binary64`
434×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1877
1	238	1462
2	529	1460
3	1344	1460
4	4947	1460
5	5050	1460

prune52.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	72	7	79

Error

0.0b

Counts

79 → 7

Alt Table

Status	Error	Program
	35.1b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	5.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	8.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	3.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
	5.2b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
	43.0b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x) 3))
▶	2.2b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

Compiler

Compiled 1276 to 381 computations (70.1% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.1b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series26.0ms (0.2%)

Counts

1 → 60

Calls

1 calls:

25.0ms

(fma.f64 (/.f64 y a) (-.f64 z t) 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:

0.0ms

(fma.f64 (/.f64 y a) (-.f64 z t) x)

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-lft-neg-out_binary64`
429×	`distribute-rgt-neg-out_binary64`
368×	`distribute-rgt-in_binary64`
367×	`distribute-lft-in_binary64`
237×	`distribute-rgt-out_binary64`

Counts

70 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	1133
1	75	750
2	165	733
3	447	733
4	2165	733
5	4627	733
6	4940	733

prune15.0ms (0.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	26	7	33

Error

0.0b

Counts

33 → 7

Alt Table

Status	Error	Program
	35.1b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	5.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	8.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	3.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
	5.2b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
	43.0b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x) 3))
✓	2.2b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

Compiler

Compiled 508 to 176 computations (65.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	0.6b	(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))
	2.1b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series716.0ms (6.8%)

Counts

3 → 180

Calls

3 calls:

496.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))

194.0ms

(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))

25.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))

1.0ms

(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))

simplify324.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

625×	`*-commutative_binary64`
281×	`associate-r_binary64`
256×	`+-commutative_binary64`
230×	`fma-def_binary64`
175×	`associate-/l*_binary64`

Counts

273 → 298

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1378	22896
1	4987	22896
2	4998	22896

prune720.0ms (6.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	586	2	588
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	588	7	595

Error

0.0b

Counts

595 → 7

Alt Table

Status	Error	Program
	33.5b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (*.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
	35.1b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	5.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	8.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))))
	5.2b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
✓	2.2b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

Compiler

Compiled 51595 to 21081 computations (59.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))))
	0.6b	(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))
	2.1b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series531.0ms (5%)

Counts

1 → 60

Calls

1 calls:

530.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`cbrt-prod_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

3.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))))

simplify202.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
403×	`*-commutative_binary64`
197×	`associate-r_binary64`
170×	`+-commutative_binary64`
130×	`sub-neg_binary64`

Counts

71 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	874	13593
1	3194	12954
2	4971	12954

prune2.0s (18.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1026	0	1026
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	1026	7	1033

Error

0.0b

Counts

1033 → 7

Alt Table

Status	Error	Program
	33.5b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (*.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
	35.1b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	5.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	8.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))))
	5.2b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
✓	2.2b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

Compiler

Compiled 127579 to 46707 computations (63.4% saved)

regimes3.4s (32%)

Accuracy

Total 0.7b remaining (97.9%)

Threshold costs 0.7b (97.9%)

Counts

177 → 3

Compiler

Compiled 61618 to 23962 computations (61.1% saved)

bsearch43.0ms (0.4%)

Steps

Iters	Range		Point
10	1.8397399884721154e-43	1.8495607931551076e-29	5.647678554096556e-33
3	-1.0494888744210892e+56	-7.2920189227617796e+50	-6.558024519895782e+52

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	26	38
2	31	38
3	33	38
4	34	38
5	34	38

end1.0ms (0%)

Compiler: Compiled 31 to 18 computations (41.9% saved)

sample976.0ms (9.3%)

Algorithm

1×

intervals

Results

356.0ms	8000×	body	128	valid
112.0ms	2506×	body	128	invalid

Compiler

Compiled 232 to 105 computations (54.7% saved)

Details

analyze1.1s (10.5%)

sample130.0ms (1.2%)

simplify66.0ms (0.6%)

prune4.0ms (0%)

localize6.0ms (0.1%)

series33.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify87.0ms (0.8%)

prune52.0ms (0.5%)

localize6.0ms (0.1%)

series26.0ms (0.2%)

rewrite1.0ms (0%)

simplify71.0ms (0.7%)

prune15.0ms (0.1%)

localize11.0ms (0.1%)

series716.0ms (6.8%)

rewrite21.0ms (0.2%)

simplify324.0ms (3.1%)

prune720.0ms (6.8%)

localize16.0ms (0.2%)

series531.0ms (5%)

rewrite3.0ms (0%)

simplify202.0ms (1.9%)

prune2.0s (18.8%)

regimes3.4s (32%)

bsearch43.0ms (0.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample976.0ms (9.3%)

Profiling