Details

analyze737.0ms (19.2%)

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
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
15.6%	80.3%	4.1%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.0s (26.3%)

Symmetry

(sort x y)

(sort z t)

Results

809.0ms	8256×	body	128	valid
138.0ms	1449×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

prune1.0ms (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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (.f64 x y) (.f64 z t))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

9.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`cancel-sign-sub-inv_binary64`
1×	`flip--_binary64`
1×	`sub-neg_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 16

Calls

1 calls:

3.0ms

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

simplify112.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

480×	`times-frac_binary64`
463×	`fma-def_binary64`
444×	`unsub-neg_binary64`
265×	`sub-neg_binary64`
232×	`distribute-rgt-neg-in_binary64`

Counts

64 → 32

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	682
1	113	658
2	347	652
3	974	652
4	2183	652
5	3451	652
6	4489	652
7	4961	652
8	4995	652
9	4859	652

prune17.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	3	33

Error

Counts

33 → 3

Alt Table

Status	Error	Program
	40.4b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))

Compiler

Compiled 562 to 154 computations (72.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))
✓	0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	1.3b	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

series244.0ms (6.4%)

Counts

3 → 144

Calls

3 calls:

119.0ms

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

94.0ms

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

31.0ms

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

rewrite44.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`
29×	`pow1_binary64`

Counts

3 → 129

Calls

3 calls:

13.0ms

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

9.0ms

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

2.0ms

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

simplify205.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

812×	`associate-/r*_binary64`
691×	`associate-/l*_binary64`
278×	`fma-def_binary64`
259×	`*-commutative_binary64`
151×	`cancel-sign-sub-inv_binary64`

Counts

273 → 349

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	644	12022
1	2159	11393
2	6015	11393

prune399.0ms (10.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	651	0	651
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	651	3	654

Error

Counts

654 → 3

Alt Table

Status	Error	Program
▶	40.4b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))

Compiler

Compiled 32784 to 11114 computations (66.1% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.7b	(+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t)))
✓	2.5b	(-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
✓	5.3b	(.f64 (.f64 x y) (*.f64 z t))
✓	39.2b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))

series285.0ms (7.4%)

Counts

4 → 192

Calls

4 calls:

162.0ms	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
69.0ms	(-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
35.0ms	(+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t)))
18.0ms	(.f64 (.f64 x y) (*.f64 z t))

rewrite59.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`prod-diff_binary64`
56×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
38×	`sqr-pow_binary64`
36×	`add-cube-cbrt_binary64`

Counts

4 → 196

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
8.0ms	(-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3))
7.0ms	(+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t)))
5.0ms	(.f64 (.f64 x y) (*.f64 z t))

simplify187.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

612×	`times-frac_binary64`
518×	`fma-neg_binary64`
396×	`associate-l_binary64`
370×	`associate-r_binary64`
247×	`exp-prod_binary64`

Counts

388 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	9918
1	623	8966
2	3184	8822
3	5004	8822

prune164.0ms (4.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	267	3	270

Error

Counts

270 → 3

Alt Table

Status	Error	Program
✓	40.4b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (*.f64 z t)))))
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))

Compiler

Compiled 14657 to 3756 computations (74.4% saved)

regimes240.0ms (6.3%)

Accuracy

Total 0.0b remaining (31.8%)

Threshold costs 0.0b (31.8%)

Counts

32 → 1

Compiler

Compiled 6075 to 3097 computations (49% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	25	10
3	31	10
4	35	10
5	36	10
6	36	10

end72.0ms (1.9%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 146 to 76 computations (47.9% saved)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Details

analyze737.0ms (19.2%)

sample1.0s (26.3%)

simplify16.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify112.0ms (2.9%)

prune17.0ms (0.4%)

localize8.0ms (0.2%)

series244.0ms (6.4%)

rewrite44.0ms (1.2%)

simplify205.0ms (5.4%)

prune399.0ms (10.4%)

localize14.0ms (0.4%)

series285.0ms (7.4%)

rewrite59.0ms (1.5%)

simplify187.0ms (4.9%)

prune164.0ms (4.3%)

regimes240.0ms (6.3%)

simplify2.0ms (0.1%)

end72.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10