Details

analyze1.3s (15.4%)

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
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.5s (18.9%)

Results

1.1s	8256×	body	128	valid
336.0ms	2663×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify65.0ms (0.8%)

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

prune3.0ms (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
▶	5.4b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	5.9b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) a)
✓	5.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series37.0ms (0.5%)

Counts

2 → 88

Calls

2 calls:

24.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)
13.0ms	(/.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:

4.0ms	(/.f64 (-.f64 z t) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)

simplify90.0ms (1.1%)

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

prune55.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Error

0.0b

Counts

79 → 6

Alt Table

Status	Error	Program
	5.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
▶	3.8b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
	4.8b	(.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)))
	43.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) (fma.f64 y (/.f64 (-.f64 z t) a) x)) (fma.f64 y (/.f64 (-.f64 z t) a) x)))
	37.4b	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) a)

Compiler

Compiled 1283 to 375 computations (70.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.6b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series23.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

23.0ms

(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)

simplify66.0ms (0.8%)

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

prune18.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	26	6	32

Error

0.0b

Counts

32 → 6

Alt Table

Status	Error	Program
	5.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
✓	3.8b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
▶	4.8b	(.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)))
	43.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) (fma.f64 y (/.f64 (-.f64 z t) a) x)) (fma.f64 y (/.f64 (-.f64 z t) a) x)))
	37.4b	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) a)

Compiler

Compiled 515 to 170 computations (67% saved)

localize9.0ms (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)))
✓	0.5b	(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))
	3.6b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series733.0ms (9%)

Counts

3 → 180

Calls

3 calls:

509.0ms

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

192.0ms

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

32.0ms

(*.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 (0.3%)

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:

8.0ms

(*.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))

simplify326.0ms (4%)

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

prune665.0ms (8.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	586	2	588
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	586	8	594

Error

0.0b

Counts

594 → 8

Alt Table

Status	Error	Program
	5.2b	(.f64 (.f64 (.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 (.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 (.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)))
	37.4b	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) a)
	5.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
✓	3.8b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
✓	4.8b	(.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)))
	43.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) (fma.f64 y (/.f64 (-.f64 z t) a) x)) (fma.f64 y (/.f64 (-.f64 z t) a) x)))
▶	5.0b	(.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)))))

Compiler

Compiled 51730 to 21110 computations (59.2% saved)

localize13.0ms (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)))
	0.5b	(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
	3.6b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series202.0ms (2.5%)

Counts

1 → 60

Calls

1 calls:

202.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 16

Calls

1 calls:

1.0ms

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

simplify125.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

639×	`associate-/l*_binary64`
587×	`associate-/r*_binary64`
388×	`fma-def_binary64`
227×	`*-commutative_binary64`
106×	`cancel-sign-sub-inv_binary64`

Counts

76 → 106

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	564	7686
1	1999	7400
2	5045	7400

prune1.4s (17.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	1031	1	1032
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	1031	9	1040

Error

0.0b

Counts

1040 → 9

Alt Table

Status	Error	Program
	5.2b	(.f64 (.f64 (.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 (.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 (.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)))
	37.4b	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) a)
	5.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
✓	3.8b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
✓	4.8b	(.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)))
	43.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) (fma.f64 y (/.f64 (-.f64 z t) a) x)) (fma.f64 y (/.f64 (-.f64 z t) a) x)))
	5.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (.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)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))))))
✓	5.0b	(.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)))))

Compiler

Compiled 121618 to 42715 computations (64.9% saved)

regimes1.3s (16.5%)

Accuracy

Total 0.7b remaining (97.4%)

Threshold costs 0.7b (97.4%)

Counts

69 → 3

Compiler

Compiled 19309 to 8122 computations (57.9% saved)

bsearch35.0ms (0.4%)

Steps

Iters	Range		Point
3	3.5186202201348e-57	4.417302791341067e-57	4.361135130640675e-57
6	-1.4436310247251774e+23	-7.882244911473868e+21	-8.821147173561544e+21

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	56
1	36	56
2	45	56
3	56	56
4	62	56
5	65	56
6	66	56
7	65	56

end119.0ms (1.5%)

Compiler: Compiled 428 to 153 computations (64.3% saved)

Details

analyze1.3s (15.4%)

sample1.5s (18.9%)

simplify65.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series37.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify90.0ms (1.1%)

prune55.0ms (0.7%)

localize6.0ms (0.1%)

series23.0ms (0.3%)

rewrite1.0ms (0%)

simplify66.0ms (0.8%)

prune18.0ms (0.2%)

localize9.0ms (0.1%)

series733.0ms (9%)

rewrite21.0ms (0.3%)

simplify326.0ms (4%)

prune665.0ms (8.1%)

localize13.0ms (0.2%)

series202.0ms (2.5%)

rewrite2.0ms (0%)

simplify125.0ms (1.5%)

prune1.4s (17.1%)

regimes1.3s (16.5%)

bsearch35.0ms (0.4%)

simplify4.0ms (0.1%)

end119.0ms (1.5%)

Profiling