Details

analyze380.0ms (9.1%)

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)

sample912.0ms (21.7%)

Symmetry

(sort y z)

Results

801.0ms	8256×	body	128	valid
52.0ms	572×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify22.0ms (0.5%)

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%)

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

3.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.6b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.4b	(.f64 x (-.f64 1 (.f64 y z)))

series8.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

8.0ms

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

rewrite6.0ms (0.1%)

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:

4.0ms

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

simplify56.0ms (1.3%)

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

prune44.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	5	51

Error

0.0b

Counts

51 → 5

Alt Table

Status	Error	Program
▶	3.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	15.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
	37.7b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	4.5b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 882 to 449 computations (49.1% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.4b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
✓	54.9b	(fma.f64 (neg.f64 z) y (*.f64 z y))

series17.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

10.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
7.0ms	(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:

2.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
0.0ms	(fma.f64 (neg.f64 z) y (*.f64 z y))

simplify56.0ms (1.3%)

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

prune79.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	57	5	62

Error

0.0b

Counts

62 → 5

Alt Table

Status	Error	Program
✓	3.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	15.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
▶	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
	37.7b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	4.5b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 1482 to 551 computations (62.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
✓	0.2b	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
✓	0.6b	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
✓	3.5b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series516.0ms (12.3%)

Counts

4 → 120

Calls

4 calls:

466.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
24.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
17.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))
10.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
40×	`flip--_binary64`
40×	`flip3--_binary64`
36×	`frac-times_binary64`

Counts

4 → 146

Calls

4 calls:

13.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
8.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
7.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
2.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))

simplify262.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

440×	`associate-/r*_binary64`
405×	`associate-l_binary64`
371×	`associate-r_binary64`
320×	`times-frac_binary64`
306×	`fma-neg_binary64`

Counts

266 → 321

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	404	8821
1	1193	7992
2	4366	7552
3	4988	7512
4	4996	7512
5	5017	7512

prune519.0ms (12.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	433	2	435
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	434	6	440

Error

0.0b

Counts

440 → 6

Alt Table

Status	Error	Program
✓	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
	11.0b	(/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 2)) x) (cbrt.f64 (-.f64 1 (.f64 (.f64 y z) (.f64 y z))))) (cbrt.f64 (+.f64 1 (*.f64 y z))))
	11.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 2)) x) (cbrt.f64 (-.f64 1 (.f64 y z))))
✓	3.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	15.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
▶	4.5b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 17839 to 10379 computations (41.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 y (.f64 z x)))
✓	6.0b	(.f64 y (.f64 z x))

series18.0ms (0.4%)

Counts

2 → 18

Calls

2 calls:

10.0ms	(.f64 y (.f64 z x))
8.0ms	(-.f64 x (.f64 y (.f64 z x)))

rewrite10.0ms (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:

4.0ms	(.f64 y (.f64 z x))
3.0ms	(-.f64 x (.f64 y (.f64 z x)))

simplify109.0ms (2.6%)

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

prune41.0ms (1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	54	7	61

Error

0.0b

Counts

61 → 7

Alt Table

Status	Error	Program
✓	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
	11.0b	(/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 2)) x) (cbrt.f64 (-.f64 1 (.f64 (.f64 y z) (.f64 y z))))) (cbrt.f64 (+.f64 1 (*.f64 y z))))
	37.8b	(.f64 (sqrt.f64 (-.f64 x (.f64 y (.f64 z x)))) (sqrt.f64 (-.f64 x (.f64 y (*.f64 z x)))))
	11.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 2)) x) (cbrt.f64 (-.f64 1 (.f64 y z))))
✓	3.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	15.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
✓	4.5b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 878 to 307 computations (65% saved)

regimes805.0ms (19.2%)

Accuracy

Total 0.1b remaining (77.1%)

Threshold costs 0.1b (77.1%)

Counts

68 → 3

Compiler

Compiled 8978 to 5869 computations (34.6% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`distribute-rgt-neg-in_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	39	48
2	61	46
3	79	46
4	86	46
5	89	46
6	87	46

end244.0ms (5.8%)

Compiler: Compiled 282 to 148 computations (47.5% 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

analyze380.0ms (9.1%)

sample912.0ms (21.7%)

simplify22.0ms (0.5%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify56.0ms (1.3%)

prune44.0ms (1.1%)

localize12.0ms (0.3%)

series17.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify56.0ms (1.3%)

prune79.0ms (1.9%)

localize9.0ms (0.2%)

series516.0ms (12.3%)

rewrite48.0ms (1.1%)

simplify262.0ms (6.2%)

prune519.0ms (12.4%)

localize4.0ms (0.1%)

series18.0ms (0.4%)

rewrite10.0ms (0.2%)

simplify109.0ms (2.6%)

prune41.0ms (1%)

regimes805.0ms (19.2%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end244.0ms (5.8%)

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