Details

analyze399.0ms (12.6%)

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
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
37.4%	59.3%	3.3%	9
45.2%	48.4%	6.4%	10
56.9%	36.7%	6.4%	11
60.5%	30.8%	8.7%	12
64.2%	24.8%	11.1%	13
70.3%	18.6%	11.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample930.0ms (29.3%)

Symmetry

(sort y z)

Results

804.0ms	8256×	body	128	valid
61.0ms	592×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify25.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-def_binary64`
121×	`fma-neg_binary64`
46×	`distribute-rgt-in_binary64`
45×	`associate-r_binary64`
43×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

4.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	4.6b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.3b	(.f64 x (-.f64 1 (.f64 y z)))

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(*.f64 x (-.f64 1 (*.f64 y z)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`prod-diff_binary64`
5×	`distribute-lft-in_binary64`
5×	`distribute-rgt-in_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 32

Calls

1 calls:

6.0ms

(*.f64 x (-.f64 1 (*.f64 y z)))

simplify55.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
608×	`distribute-neg-out_binary64`
586×	`unsub-neg_binary64`
290×	`associate-l_binary64`
267×	`*-commutative_binary64`

Counts

68 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	843
1	139	783
2	446	747
3	1293	729
4	2542	729
5	4900	729

prune32.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Error

0.0b

Counts

51 → 5

Alt Table

Status	Error	Program
	35.8b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
▶	4.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	23.8b	(expm1.f64 (log1p.f64 (.f64 x (-.f64 1 (.f64 y z)))))
	5.3b	(-.f64 x (.f64 y (.f64 z x)))
✓	4.6b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 818 to 410 computations (49.9% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.3b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
✓	50.9b	(fma.f64 (neg.f64 z) y (*.f64 z y))

series17.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

8.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
8.0ms	(fma.f64 (neg.f64 z) y (*.f64 z y))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

3.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
0.0ms	(fma.f64 (neg.f64 z) y (*.f64 z y))

simplify57.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
629×	`distribute-rgt-neg-out_binary64`
627×	`distribute-rgt-in_binary64`
578×	`distribute-lft-in_binary64`
387×	`distribute-neg-out_binary64`

Counts

90 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	777
1	109	708
2	294	652
3	881	652
4	2988	652
5	5214	652

prune37.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	57	5	62

Error

0.0b

Counts

62 → 5

Alt Table

Status	Error	Program
	35.8b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
✓	4.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	23.8b	(expm1.f64 (log1p.f64 (.f64 x (-.f64 1 (.f64 y z)))))
▶	5.3b	(-.f64 x (.f64 y (.f64 z x)))
✓	4.6b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 1418 to 512 computations (63.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 y (.f64 z x)))
✓	5.6b	(.f64 y (.f64 z x))

series17.0ms (0.5%)

Counts

2 → 18

Calls

2 calls:

10.0ms	(.f64 y (.f64 z x))
7.0ms	(-.f64 x (.f64 y (.f64 z x)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(.f64 y (.f64 z x))
2.0ms	(-.f64 x (.f64 y (.f64 z x)))

simplify116.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-def_binary64`
462×	`fma-neg_binary64`
392×	`distribute-rgt-neg-in_binary64`
378×	`distribute-lft-neg-in_binary64`
300×	`distribute-rgt-in_binary64`

Counts

58 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	682
1	195	637
2	585	609
3	1582	608
4	4260	608
5	4932	608
6	4986	608
7	4996	608
8	4794	608

prune34.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	54	6	60

Error

0.0b

Counts

60 → 6

Alt Table

Status	Error	Program
	35.8b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
✓	4.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	23.8b	(expm1.f64 (log1p.f64 (.f64 x (-.f64 1 (.f64 y z)))))
✓	5.3b	(-.f64 x (.f64 y (.f64 z x)))
▶	5.7b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))
	26.1b	(-.f64 x (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (*.f64 z x)))))

Compiler

Compiled 886 to 308 computations (65.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	2.8b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))
✓	3.0b	(.f64 (cbrt.f64 y) (.f64 z x))

series541.0ms (17%)

Counts

4 → 96

Calls

4 calls:

429.0ms	(.f64 (cbrt.f64 y) (.f64 z x))
59.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
30.0ms	(cbrt.f64 y)
22.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 108

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))
4.0ms	(.f64 (cbrt.f64 y) (.f64 z x))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
2.0ms	(cbrt.f64 y)

simplify139.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
621×	`distribute-rgt-in_binary64`
464×	`*-commutative_binary64`
327×	`sqr-pow_binary64`
233×	`associate-l_binary64`

Counts

204 → 137

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	1885
1	239	1657
2	914	1619
3	1620	1605
4	2950	1511
5	4929	1511

prune148.0ms (4.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	173	6	179

Error

Counts

179 → 6

Alt Table

Status	Error	Program
	15.5b	(-.f64 x (.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 z x))))
✓	5.7b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))
✓	4.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	23.8b	(expm1.f64 (log1p.f64 (.f64 x (-.f64 1 (.f64 y z)))))
✓	5.3b	(-.f64 x (.f64 y (.f64 z x)))
	26.1b	(-.f64 x (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (*.f64 z x)))))

Compiler

Compiled 3284 to 833 computations (74.6% saved)

regimes304.0ms (9.6%)

Accuracy

Total 0.1b remaining (79.8%)

Threshold costs 0.1b (79.8%)

Counts

25 → 3

Compiler

Compiled 2818 to 1668 computations (40.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	43	61
2	63	61
3	73	61
4	78	61
5	79	61
6	78	61

end236.0ms (7.4%)

Compiler: Compiled 271 to 135 computations (50.2% saved)

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

Details

analyze399.0ms (12.6%)

sample930.0ms (29.3%)

simplify25.0ms (0.8%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite8.0ms (0.2%)

simplify55.0ms (1.7%)

prune32.0ms (1%)

localize11.0ms (0.3%)

series17.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify57.0ms (1.8%)

prune37.0ms (1.2%)

localize5.0ms (0.2%)

series17.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify116.0ms (3.7%)

prune34.0ms (1.1%)

localize8.0ms (0.3%)

series541.0ms (17%)

rewrite24.0ms (0.8%)

simplify139.0ms (4.4%)

prune148.0ms (4.7%)

regimes304.0ms (9.6%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end236.0ms (7.4%)

Profiling

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10