Details

analyze91.0ms (2.8%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample851.0ms (26.3%)

Results

776.0ms	8256×	body	128	valid
12.0ms	154×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify24.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
148×	`fma-neg_binary64`
84×	`distribute-rgt-in_binary64`
50×	`distribute-lft-in_binary64`
50×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

series6.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
16×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 51

Calls

1 calls:

7.0ms

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

simplify149.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-neg_binary64`
433×	`exp-prod_binary64`
400×	`*-commutative_binary64`
343×	`fma-def_binary64`
288×	`associate-+r+_binary64`

Counts

75 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1085
1	223	985
2	948	871
3	2323	814
4	4186	814
5	4991	814
6	4915	814
7	4901	814

prune64.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Error

0.0b

Counts

74 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
▶	0.4b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y)))
	33.8b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 x y)))
	5.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	35.3b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	9.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	0.5b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))

Compiler

Compiled 1482 to 648 computations (56.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y))
✓	0.2b	(.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)

series109.0ms (3.4%)

Counts

4 → 60

Calls

4 calls:

36.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
34.0ms	(cbrt.f64 y)
23.0ms	(.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y))
15.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 108

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
5.0ms	(.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y))
4.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify122.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
503×	`log-prod_binary64`
491×	`exp-prod_binary64`
473×	`*-commutative_binary64`
405×	`cube-prod_binary64`

Counts

168 → 159

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	122	1582
1	269	1447
2	1151	1376
3	2648	1343
4	4095	1331
5	4890	1331
6	4929	1331

prune210.0ms (6.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	197	7	204

Error

0.0b

Counts

204 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
✓	0.4b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y)))
	33.8b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 x y)))
	5.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	35.3b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	9.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
▶	0.5b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))

Compiler

Compiled 4798 to 1664 computations (65.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
✓	0.2b	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
✓	0.2b	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
✓	0.2b	(cbrt.f64 (-.f64 1 y))

series353.0ms (10.9%)

Counts

4 → 72

Calls

4 calls:

337.0ms	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
8.0ms	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
4.0ms	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
4.0ms	(cbrt.f64 (-.f64 1 y))

rewrite59.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
44×	`cbrt-prod_binary64`
41×	`add-sqr-sqrt_binary64`
41×	`pow1_binary64`

Counts

4 → 172

Calls

4 calls:

18.0ms	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
11.0ms	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
9.0ms	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
2.0ms	(cbrt.f64 (-.f64 1 y))

simplify145.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
549×	`associate-l_binary64`
390×	`associate-r_binary64`
385×	`fma-neg_binary64`
325×	`cancel-sign-sub-inv_binary64`

Counts

244 → 288

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	300	5299
1	760	4846
2	2552	4532
3	4553	4507
4	4984	4507

prune397.0ms (12.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	376	0	376
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	376	7	383

Error

0.0b

Counts

383 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
✓	0.4b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y)))
	33.8b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 x y)))
▶	5.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	35.3b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	9.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.5b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))

Compiler

Compiled 10644 to 7429 computations (30.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (pow.f64 y 2))
✓	5.5b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

series11.0ms (0.3%)

Counts

2 → 15

Calls

2 calls:

9.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
2.0ms	(-.f64 y (pow.f64 y 2))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
24×	`prod-diff_binary64`
21×	`add-cube-cbrt_binary64`
14×	`unpow-prod-down_binary64`

Counts

2 → 82

Calls

2 calls:

7.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
5.0ms	(-.f64 y (pow.f64 y 2))

simplify95.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

967×	`fma-neg_binary64`
456×	`fma-def_binary64`
377×	`exp-prod_binary64`
263×	`cancel-sign-sub-inv_binary64`
232×	`difference-of-squares_binary64`

Counts

97 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1889
1	261	1074
2	791	924
3	2087	924
4	3779	924
5	4661	924
6	4794	924

prune96.0ms (3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	124	7	131

Error

0.0b

Counts

131 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
✓	0.4b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y)))
	33.8b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 x y)))
✓	5.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	35.3b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	9.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.5b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))

Compiler

Compiled 2290 to 1260 computations (45% saved)

regimes244.0ms (7.5%)

Accuracy

Total 0.1b remaining (77.4%)

Threshold costs 0.1b (77.4%)

Counts

86 → 1

Compiler

Compiled 4572 to 2933 computations (35.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	21	15
2	36	13
3	44	13
4	49	13
5	51	13
6	49	13

end122.0ms (3.8%)

Compiler: Compiled 128 to 79 computations (38.3% saved)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Details

analyze91.0ms (2.8%)

sample851.0ms (26.3%)

simplify24.0ms (0.8%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite11.0ms (0.3%)

simplify149.0ms (4.6%)

prune64.0ms (2%)

localize12.0ms (0.4%)

series109.0ms (3.4%)

rewrite25.0ms (0.8%)

simplify122.0ms (3.8%)

prune210.0ms (6.5%)

localize8.0ms (0.3%)

series353.0ms (10.9%)

rewrite59.0ms (1.8%)

simplify145.0ms (4.5%)

prune397.0ms (12.3%)

localize5.0ms (0.2%)

series11.0ms (0.3%)

rewrite16.0ms (0.5%)

simplify95.0ms (2.9%)

prune96.0ms (3%)

regimes244.0ms (7.5%)

simplify2.0ms (0.1%)

end122.0ms (3.8%)

Profiling

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10