Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.1s (19.3%)

Infinites

16.1% of outputs are infinite.

Symmetry

(sort y z)

Results

994.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify44.0ms (0.7%)

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

prune3.0ms (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

2.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.0b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(.f64 x (-.f64 1 (.f64 y z)))

series23.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

23.0ms

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

rewrite12.0ms (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:

9.0ms

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

simplify107.0ms (1.8%)

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

prune76.0ms (1.3%)

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
	10.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	16.0b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
▶	2.3b	(.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))))
	35.4b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	3.9b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 882 to 449 computations (49.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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))))
✓	1.0b	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
✓	7.8b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series948.0ms (16.1%)

Counts

4 → 120

Calls

4 calls:

847.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
47.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
32.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))
21.0ms	(.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))))

rewrite111.0ms (1.9%)

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:

31.0ms	(.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))))
20.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
17.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
4.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))

simplify488.0ms (8.3%)

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

prune814.0ms (13.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	435	0	435
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	435	5	440

Error

0.0b

Counts

440 → 5

Alt Table

Status	Error	Program
	10.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	16.0b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
✓	2.3b	(.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))))
	35.4b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
▶	3.9b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 17799 to 10352 computations (41.8% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.2b	(.f64 y (.f64 z x))

series16.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

16.0ms

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

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

8.0ms

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

simplify104.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

580×	`log-div_binary64`
514×	`associate-/l*_binary64`
411×	`*-commutative_binary64`
409×	`associate-l_binary64`
339×	`cube-div_binary64`

Counts

20 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	219
1	87	174
2	275	174
3	770	174
4	976	174
5	1185	174
6	1422	174
7	1902	174
8	3020	174
9	4714	174
10	4982	174

prune40.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	17	3	20
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	18	7	25

Error

Counts

25 → 7

Alt Table

Status	Error	Program
	46.5b	(-.f64 x (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 z x))))
	26.8b	(-.f64 x (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (*.f64 z x)))))
	10.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
✓	2.3b	(.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))))
	35.4b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
✓	3.9b	(-.f64 x (.f64 y (.f64 z x)))
▶	4.2b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))

Compiler

Compiled 466 to 208 computations (55.4% saved)

localize15.0ms (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)
✓	2.2b	(.f64 (cbrt.f64 y) (.f64 z x))
✓	3.2b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))

series680.0ms (11.6%)

Counts

4 → 96

Calls

4 calls:

574.0ms	(.f64 (cbrt.f64 y) (.f64 z x))
41.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))
36.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
29.0ms	(cbrt.f64 y)

rewrite25.0ms (0.4%)

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:

10.0ms	(.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))
1.0ms	(cbrt.f64 y)

simplify90.0ms (1.5%)

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 → 146

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

prune129.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	182	7	189

Error

Counts

189 → 7

Alt Table

Status	Error	Program
	3.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 (cbrt.f64 y) z) x)))
	10.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
✓	2.3b	(.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))))
	35.4b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	26.8b	(-.f64 x (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (*.f64 z x)))))
✓	3.9b	(-.f64 x (.f64 y (.f64 z x)))
✓	4.2b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))

Compiler

Compiled 3485 to 894 computations (74.3% saved)

regimes764.0ms (13%)

Accuracy

Total 1.2b remaining (98%)

Threshold costs 0b (0%)

Counts

62 → 2

Compiler

Compiled 8021 to 5327 computations (33.6% saved)

bsearch3.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	30
1	32	30
2	48	28
3	67	28
4	81	28
5	85	28
6	86	28
7	84	28

end201.0ms (3.4%)

Remove: (sort y z)
Compiler: Compiled 217 to 122 computations (43.8% 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

analyze4.0ms (0.1%)

sample1.1s (19.3%)

simplify44.0ms (0.7%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series23.0ms (0.4%)

rewrite12.0ms (0.2%)

simplify107.0ms (1.8%)

prune76.0ms (1.3%)

localize18.0ms (0.3%)

series948.0ms (16.1%)

rewrite111.0ms (1.9%)

simplify488.0ms (8.3%)

prune814.0ms (13.8%)

localize8.0ms (0.1%)

series16.0ms (0.3%)

rewrite10.0ms (0.2%)

simplify104.0ms (1.8%)

prune40.0ms (0.7%)

localize15.0ms (0.3%)

series680.0ms (11.6%)

rewrite25.0ms (0.4%)

simplify90.0ms (1.5%)

prune129.0ms (2.2%)

regimes764.0ms (13%)

bsearch3.0ms (0.1%)

simplify7.0ms (0.1%)

end201.0ms (3.4%)

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