Details

analyze950.0ms (27.2%)

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
13.3%	86.5%	0.2%	9
17.5%	82.3%	0.2%	10
23.6%	75.2%	1.2%	11
25%	72%	2.9%	12
35.8%	59.6%	4.6%	13
40.3%	54.3%	5.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.4s (39%)

Results

914.0ms	8256×	body	128	valid
244.0ms	2269×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify64.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
721×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
144×	`distribute-rgt-in_binary64`
108×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	37	11
3	72	11
4	140	11
5	242	11
6	395	11
7	682	11
8	1049	11
9	1368	11
10	1492	11
11	1530	11
12	1536	11
13	1541	11
14	1541	11
15	1456	11

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

2.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.1b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
▶	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 71 to 39 computations (45.1% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series16.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

16.0ms

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

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 x y) (-.f64 z t) t)

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

550×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
356×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`
297×	`times-frac_binary64`

Counts

58 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	730
1	85	635
2	196	623
3	466	623
4	2285	623
5	4620	623
6	5293	623

prune16.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Error

0.0b

Counts

25 → 4

Alt Table

Status	Error	Program
	42.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t) (fma.f64 (/.f64 x y) (-.f64 z t) t)) (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	35.9b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
▶	6.1b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 388 to 123 computations (68.3% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 t (/.f64 (*.f64 z x) y))
✓	5.5b	(/.f64 (*.f64 z x) y)
✓	7.2b	(/.f64 (*.f64 t x) y)

series35.0ms (1%)

Counts

3 → 12

Calls

3 calls:

13.0ms	(+.f64 t (/.f64 (*.f64 z x) y))
12.0ms	(/.f64 (*.f64 t x) y)
11.0ms	(/.f64 (*.f64 z x) y)

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

4.0ms	(/.f64 (*.f64 z x) y)
3.0ms	(+.f64 t (/.f64 (*.f64 z x) y))
3.0ms	(/.f64 (*.f64 t x) y)

simplify86.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

875×	`fma-def_binary64`
770×	`associate-/l*_binary64`
705×	`times-frac_binary64`
336×	`associate-*l/_binary64`
316×	`associate-/l/_binary64`

Counts

75 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	762
1	269	696
2	913	670
3	3936	670
4	4769	670
5	4964	670
6	4998	670
7	4960	670

prune49.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	89	6	95

Error

0.0b

Counts

95 → 6

Alt Table

Status	Error	Program
	35.9b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
✓	6.1b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
	32.4b	(-.f64 (fma.f64 (sqrt.f64 t) (sqrt.f64 t) (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
▶	6.1b	(-.f64 (+.f64 t (.f64 (.f64 z x) (/.f64 1 y))) (/.f64 (*.f64 t x) y))
	6.1b	(-.f64 (+.f64 t (/.f64 1 (/.f64 y (.f64 z x)))) (/.f64 (.f64 t x) y))
✓	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 1821 to 470 computations (74.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 t (.f64 (.f64 z x) (/.f64 1 y)))
✓	5.5b	(.f64 (.f64 z x) (/.f64 1 y))
	7.2b	(/.f64 (*.f64 t x) y)

series24.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

12.0ms	(.f64 (.f64 z x) (/.f64 1 y))
11.0ms	(+.f64 t (.f64 (.f64 z x) (/.f64 1 y)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`prod-exp_binary64`
10×	`*-un-lft-identity_binary64`

Counts

2 → 56

Calls

2 calls:

6.0ms	(.f64 (.f64 z x) (/.f64 1 y))
2.0ms	(+.f64 t (.f64 (.f64 z x) (/.f64 1 y)))

simplify77.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

751×	`times-frac_binary64`
391×	`associate-/r*_binary64`
335×	`fma-neg_binary64`
318×	`associate-/l/_binary64`
301×	`associate-/r/_binary64`

Counts

140 → 83

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	92	1238
1	234	1118
2	779	1118
3	2178	1118
4	4858	1118
5	5014	1118

prune84.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	119	6	125

Error

0.0b

Counts

125 → 6

Alt Table

Status	Error	Program
	35.9b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
✓	6.1b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
	32.4b	(-.f64 (fma.f64 (sqrt.f64 t) (sqrt.f64 t) (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	6.1b	(-.f64 (+.f64 t (.f64 (.f64 z x) (/.f64 1 y))) (/.f64 (*.f64 t x) y))
▶	6.1b	(-.f64 (+.f64 t (/.f64 1 (/.f64 y (.f64 z x)))) (/.f64 (.f64 t x) y))
✓	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 2579 to 996 computations (61.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 t (/.f64 1 (/.f64 y (*.f64 z x))))
✓	0.7b	(/.f64 1 (/.f64 y (*.f64 z x)))
✓	5.4b	(/.f64 y (*.f64 z x))
	7.2b	(/.f64 (*.f64 t x) y)

series40.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

15.0ms	(/.f64 y (*.f64 z x))
12.0ms	(+.f64 t (/.f64 1 (/.f64 y (*.f64 z x))))
12.0ms	(/.f64 1 (/.f64 y (*.f64 z x)))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
29×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`

Counts

3 → 99

Calls

3 calls:

8.0ms	(+.f64 t (/.f64 1 (/.f64 y (*.f64 z x))))
5.0ms	(/.f64 1 (/.f64 y (*.f64 z x)))
3.0ms	(/.f64 y (*.f64 z x))

simplify115.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
672×	`fma-neg_binary64`
358×	`associate-/l*_binary64`
320×	`associate-/r*_binary64`
276×	`associate-r_binary64`

Counts

183 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	1975
1	250	1772
2	799	1645
3	3377	1645
4	4399	1645
5	4862	1645
6	5050	1645

prune117.0ms (3.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	164	7	171

Error

Counts

171 → 7

Alt Table

Status	Error	Program
	7.8b	(-.f64 (+.f64 t (/.f64 1 (/.f64 (/.f64 y z) x))) (/.f64 (*.f64 t x) y))
✓	6.1b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
	35.9b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	32.4b	(-.f64 (fma.f64 (sqrt.f64 t) (sqrt.f64 t) (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	6.1b	(-.f64 (+.f64 t (.f64 (.f64 z x) (/.f64 1 y))) (/.f64 (*.f64 t x) y))
✓	6.1b	(-.f64 (+.f64 t (/.f64 1 (/.f64 y (.f64 z x)))) (/.f64 (.f64 t x) y))
✓	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 3491 to 1179 computations (66.2% saved)

regimes172.0ms (4.9%)

Accuracy

Total 1.4b remaining (98.9%)

Threshold costs 0b (0%)

Counts

21 → 3

Compiler

Compiled 2092 to 1227 computations (41.3% saved)

bsearch41.0ms (1.2%)

Steps

Iters	Range		Point
6	6.013948439158708e-22	5.6893671974805484e-21	3.791419667085907e-21
8	-2.857040973080259e-87	-6.131719265960262e-91	-2.809238893075622e-87

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-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	23	55
1	32	55
2	42	55
3	53	55
4	59	55
5	62	55
6	63	55
7	63	55

end92.0ms (2.6%)

Compiler: Compiled 203 to 114 computations (43.8% saved)

Details

analyze950.0ms (27.2%)

sample1.4s (39%)

simplify64.0ms (1.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series16.0ms (0.5%)

rewrite1.0ms (0%)

simplify65.0ms (1.9%)

prune16.0ms (0.5%)

localize9.0ms (0.3%)

series35.0ms (1%)

rewrite12.0ms (0.3%)

simplify86.0ms (2.5%)

prune49.0ms (1.4%)

localize10.0ms (0.3%)

series24.0ms (0.7%)

rewrite12.0ms (0.3%)

simplify77.0ms (2.2%)

prune84.0ms (2.4%)

localize10.0ms (0.3%)

series40.0ms (1.1%)

rewrite20.0ms (0.6%)

simplify115.0ms (3.3%)

prune117.0ms (3.4%)

regimes172.0ms (4.9%)

bsearch41.0ms (1.2%)

simplify4.0ms (0.1%)

end92.0ms (2.6%)

Profiling