Details

analyze1.2s (17.2%)

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)

sample1.4s (19.8%)

Results

988.0ms	8256×	body	128	valid
312.0ms	2762×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify69.0ms (1%)

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
	7.9b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	6.7b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

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)
✓	6.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series36.0ms (0.5%)

Counts

2 → 88

Calls

2 calls:

26.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)
10.0ms	(/.f64 (-.f64 z t) a)

rewrite8.0ms (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)

simplify90.0ms (1.3%)

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

prune49.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	73	6	79

Error

0.0b

Counts

79 → 6

Alt Table

Status	Error	Program
	7.2b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a)) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
	38.0b	(fma.f64 y (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) a)) x)
▶	2.3b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	7.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	6.7b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

Compiler

Compiled 1260 to 365 computations (71% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series59.0ms (0.8%)

Counts

1 → 60

Calls

1 calls:

59.0ms

(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)

simplify67.0ms (0.9%)

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

prune14.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	26	6	32

Error

0.0b

Counts

32 → 6

Alt Table

Status	Error	Program
▶	7.2b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a)) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
	38.0b	(fma.f64 y (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) a)) x)
✓	2.3b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	7.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	6.7b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

Compiler

Compiled 492 to 160 computations (67.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
✓	0.6b	(cbrt.f64 (-.f64 z t))
✓	6.3b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a)) x)

series125.0ms (1.8%)

Counts

4 → 144

Calls

4 calls:

38.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
36.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a)) x)
30.0ms	(cbrt.f64 (-.f64 z t))
21.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
49×	`cbrt-prod_binary64`
38×	`cbrt-div_binary64`
36×	`associate-r_binary64`

Counts

4 → 154

Calls

4 calls:

16.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a))
10.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
2.0ms	(cbrt.f64 (-.f64 z t))
0.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a)) x)

simplify137.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-def_binary64`
594×	`times-frac_binary64`
419×	`associate-l_binary64`
394×	`associate-r_binary64`
235×	`*-commutative_binary64`

Counts

298 → 290

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	390	6198
1	993	5615
2	3395	5374
3	5117	5374

prune259.0ms (3.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	392	0	392
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	392	6	398

Error

0.0b

Counts

398 → 6

Alt Table

Status	Error	Program
✓	7.2b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a)) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
	38.0b	(fma.f64 y (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) a)) x)
✓	2.3b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
▶	7.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	6.7b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

Compiler

Compiled 12181 to 4216 computations (65.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	0.5b	(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))
	6.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series986.0ms (13.9%)

Counts

3 → 180

Calls

3 calls:

760.0ms

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

196.0ms

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

29.0ms

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

7.0ms

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

5.0ms

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

1.0ms

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

simplify349.0ms (4.9%)

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	1379	22713
1	4987	22713
2	4998	22713

prune649.0ms (9.1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	600	3	603
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	600	9	609

Error

0.0b

Counts

609 → 9

Alt Table

Status	Error	Program
	38.0b	(fma.f64 y (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) a)) x)
	8.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	7.2b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) a)) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
✓	2.3b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	10.5b	(.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	7.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
✓	6.7b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	8.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x))))

Compiler

Compiled 51916 to 21108 computations (59.3% saved)

regimes1.3s (19%)

Accuracy

Total 0.7b remaining (97.7%)

Threshold costs 0.7b (97.7%)

Counts

79 → 3

Compiler

Compiled 19932 to 9479 computations (52.4% saved)

bsearch3.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% 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	25	65
1	33	65
2	43	65
3	54	65
4	60	65
5	63	65
6	64	65
7	64	65

end115.0ms (1.6%)

Compiler: Compiled 391 to 146 computations (62.7% saved)

Details

analyze1.2s (17.2%)

sample1.4s (19.8%)

simplify69.0ms (1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series36.0ms (0.5%)

rewrite8.0ms (0.1%)

simplify90.0ms (1.3%)

prune49.0ms (0.7%)

localize6.0ms (0.1%)

series59.0ms (0.8%)

rewrite1.0ms (0%)

simplify67.0ms (0.9%)

prune14.0ms (0.2%)

localize9.0ms (0.1%)

series125.0ms (1.8%)

rewrite47.0ms (0.7%)

simplify137.0ms (1.9%)

prune259.0ms (3.6%)

localize10.0ms (0.1%)

series986.0ms (13.9%)

rewrite21.0ms (0.3%)

simplify349.0ms (4.9%)

prune649.0ms (9.1%)

regimes1.3s (19%)

bsearch3.0ms (0%)

simplify4.0ms (0.1%)

end115.0ms (1.6%)

Profiling