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 (14.2%)

Symmetry

(sort y z)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify37.0ms (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

2.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.2b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(.f64 x (-.f64 1 (.f64 y z)))

series16.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

16.0ms

(*.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)))

simplify119.0ms (1.5%)

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

prune84.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
	6.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	32.9b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
▶	3.2b	(-.f64 x (.f64 y (.f64 z x)))
✓	2.2b	(.f64 x (-.f64 1 (.f64 y z)))
	3.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	12.5b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))

Compiler

Compiled 880 to 442 computations (49.8% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 y (.f64 z x)))
✓	4.4b	(.f64 y (.f64 z x))

series34.0ms (0.4%)

Counts

2 → 18

Calls

2 calls:

17.0ms	(-.f64 x (.f64 y (.f64 z x)))
17.0ms	(.f64 y (.f64 z x))

rewrite19.0ms (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:

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

simplify205.0ms (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

prune81.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	53	8	61

Error

0.0b

Counts

61 → 8

Alt Table

Status	Error	Program
	3.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))))
▶	3.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	6.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	32.9b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
✓	3.2b	(-.f64 x (.f64 y (.f64 z x)))
✓	2.2b	(.f64 x (-.f64 1 (.f64 y z)))
	3.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))
	12.5b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))

Compiler

Compiled 994 to 362 computations (63.6% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
✓	1.3b	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z)))

series446.0ms (5.7%)

Counts

4 → 96

Calls

4 calls:

251.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z)))
77.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
73.0ms	(cbrt.f64 x)
45.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`

Counts

4 → 137

Calls

4 calls:

21.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
10.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z)))
8.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify209.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

495×	`distribute-rgt-neg-out_binary64`
401×	`fma-def_binary64`
332×	`associate-l_binary64`
321×	`distribute-rgt-in_binary64`
300×	`distribute-lft-in_binary64`

Counts

233 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	165	2930
1	325	2617
2	1291	2456
3	3232	2351
4	4775	2351
5	4674	2351

prune227.0ms (2.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	230	8	238

Error

0.0b

Counts

238 → 8

Alt Table

Status	Error	Program
▶	3.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))))
✓	3.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	6.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	32.9b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
✓	3.2b	(-.f64 x (.f64 y (.f64 z x)))
✓	2.2b	(.f64 x (-.f64 1 (.f64 y z)))
	3.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))
	12.5b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))

Compiler

Compiled 4881 to 1774 computations (63.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (*.f64 z x))))
	4.4b	(.f64 y (.f64 z x))
✓	19.6b	(cbrt.f64 (.f64 y (.f64 z x)))

series3.7s (47.6%)

Counts

3 → 108

Calls

3 calls:

2.4s

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

1.2s

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

105.0ms

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

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

15.0ms

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

15.0ms

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

5.0ms

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

simplify175.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

640×	`unswap-sqr_binary64`
348×	`fma-neg_binary64`
314×	`exp-sum_binary64`
297×	`exp-prod_binary64`
260×	`unsub-neg_binary64`

Counts

187 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	3163
1	387	2879
2	865	2337
3	2290	2071
4	5245	2071

prune276.0ms (3.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	229	9	238

Error

0.0b

Counts

238 → 9

Alt Table

Status	Error	Program
	32.9b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	3.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))))))
✓	3.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))))
✓	3.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	6.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
✓	3.2b	(-.f64 x (.f64 y (.f64 z x)))
✓	2.2b	(.f64 x (-.f64 1 (.f64 y z)))
	3.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))
	12.5b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))

Compiler

Compiled 6209 to 1367 computations (78% saved)

regimes492.0ms (6.3%)

Accuracy

Total 1.2b remaining (98.4%)

Threshold costs 0b (0%)

Counts

31 → 3

Compiler

Compiled 3833 to 2205 computations (42.5% saved)

bsearch22.0ms (0.3%)

Steps

Iters	Range		Point
5	3.5554107917167987e+34	2.9518931733082763e+41	1.5506037414681654e+35
1	-4.938560316356167e-17	-4.893747819988189e-28	-1.5833889410078922e-22

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	36	34
2	51	34
3	66	34
4	75	34
5	79	34
6	80	34
7	79	34

end360.0ms (4.6%)

Remove: (sort y z)
Compiler: Compiled 285 to 157 computations (44.9% 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 (14.2%)

simplify37.0ms (0.5%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series16.0ms (0.2%)

rewrite12.0ms (0.2%)

simplify119.0ms (1.5%)

prune84.0ms (1.1%)

localize13.0ms (0.2%)

series34.0ms (0.4%)

rewrite19.0ms (0.2%)

simplify205.0ms (2.6%)

prune81.0ms (1%)

localize23.0ms (0.3%)

series446.0ms (5.7%)

rewrite56.0ms (0.7%)

simplify209.0ms (2.7%)

prune227.0ms (2.9%)

localize16.0ms (0.2%)

series3.7s (47.6%)

rewrite45.0ms (0.6%)

simplify175.0ms (2.2%)

prune276.0ms (3.5%)

regimes492.0ms (6.3%)

bsearch22.0ms (0.3%)

simplify8.0ms (0.1%)

end360.0ms (4.6%)

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