Details

analyze179.0ms (2.1%)

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
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)

sample1.4s (16.9%)

Results

1.3s	8256×	body	128	valid
32.0ms	222×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify35.0ms (0.4%)

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

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

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)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series14.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

14.0ms

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

rewrite23.0ms (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:

15.0ms

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

simplify147.0ms (1.7%)

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

prune102.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Error

0.0b

Counts

74 → 6

Alt Table

Status	Error	Program
	29.6b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
▶	0.1b	(.f64 (.f64 y x) (-.f64 1 y))
	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	13.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	0.6b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
	30.2b	(.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (sqrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))

Compiler

Compiled 1453 to 636 computations (56.2% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series14.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

14.0ms

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

rewrite20.0ms (0.2%)

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:

13.0ms

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

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-neg_binary64`
480×	`associate-+l+_binary64`
394×	`*-commutative_binary64`
264×	`fma-def_binary64`
247×	`associate-l_binary64`

Counts

75 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1085
1	222	986
2	938	873
3	2263	817
4	4385	817
5	4767	817

prune153.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Error

0.0b

Counts

76 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 y x) (-.f64 1 y))
	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	13.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
▶	0.6b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
	29.6b	(.f64 (.f64 y (fma.f64 x (sqrt.f64 y) x)) (-.f64 1 (sqrt.f64 y)))
	30.2b	(.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (sqrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))

Compiler

Compiled 1406 to 602 computations (57.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series625.0ms (7.3%)

Counts

4 → 72

Calls

4 calls:

595.0ms	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
15.0ms	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
7.0ms	(cbrt.f64 (-.f64 1 y))
7.0ms	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))

rewrite126.0ms (1.5%)

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:

37.0ms	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
24.0ms	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
20.0ms	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
5.0ms	(cbrt.f64 (-.f64 1 y))

simplify267.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
549×	`associate-l_binary64`
392×	`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	4491
4	4984	4491

prune829.0ms (9.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	371	5	376
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	373	9	382

Error

Counts

382 → 9

Alt Table

Status	Error	Program
	45.0b	(.f64 (.f64 x (cbrt.f64 (pow.f64 y 5))) (cbrt.f64 (-.f64 1 y)))
▶	0.6b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))) (cbrt.f64 (-.f64 1 y)))))
✓	0.1b	(.f64 (.f64 y x) (-.f64 1 y))
	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	13.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	29.6b	(.f64 (.f64 y (fma.f64 x (sqrt.f64 y) x)) (-.f64 1 (sqrt.f64 y)))
	0.9b	(.f64 (.f64 y (.f64 x (.f64 (cbrt.f64 (-.f64 1 y)) (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 y))) 5)))) (cbrt.f64 (cbrt.f64 (-.f64 1 y))))
	3.8b	(.f64 (.f64 x (.f64 y (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))) (cbrt.f64 (-.f64 1 y)))
	0.8b	(.f64 (.f64 (.f64 x y) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 y))) 5) (cbrt.f64 (cbrt.f64 (-.f64 1 y))))) (cbrt.f64 (-.f64 1 y)))

Compiler

Compiled 10786 to 7538 computations (30.1% saved)

localize20.0ms (0.2%)

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 (.f64 (cbrt.f64 (-.f64 1 y)) (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 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))) (cbrt.f64 (-.f64 1 y))))
	0.2b	(cbrt.f64 (-.f64 1 y))

series24.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

17.0ms

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

7.0ms

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

rewrite367.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

1124×	`cbrt-div_binary64`
596×	`frac-times_binary64`
432×	`flip--_binary64`
432×	`flip3--_binary64`
376×	`associate-*r/_binary64`

Counts

2 → 310

Calls

2 calls:

51.0ms

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

24.0ms

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

simplify812.0ms (9.5%)

Algorithm

1×	egg-herbie

Rules

1017×	`associate-l_binary64`
540×	`*-commutative_binary64`
508×	`associate-r_binary64`
418×	`fma-def_binary64`
332×	`fma-neg_binary64`

Counts

346 → 424

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	570	22448
1	925	22302
2	2734	22253
3	4758	22253
4	5008	22253

prune2.5s (29.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	830	0	830
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	830	9	839

Error

Counts

839 → 9

Alt Table

Status	Error	Program
	45.0b	(.f64 (.f64 x (cbrt.f64 (pow.f64 y 5))) (cbrt.f64 (-.f64 1 y)))
✓	0.6b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))) (cbrt.f64 (-.f64 1 y)))))
✓	0.1b	(.f64 (.f64 y x) (-.f64 1 y))
	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	13.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	29.6b	(.f64 (.f64 y (fma.f64 x (sqrt.f64 y) x)) (-.f64 1 (sqrt.f64 y)))
	0.9b	(.f64 (.f64 y (.f64 x (.f64 (cbrt.f64 (-.f64 1 y)) (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 y))) 5)))) (cbrt.f64 (cbrt.f64 (-.f64 1 y))))
	3.8b	(.f64 (.f64 x (.f64 y (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))) (cbrt.f64 (-.f64 1 y)))
	0.8b	(.f64 (.f64 (.f64 x y) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 y))) 5) (cbrt.f64 (cbrt.f64 (-.f64 1 y))))) (cbrt.f64 (-.f64 1 y)))

Compiler

Compiled 41313 to 30139 computations (27% saved)

regimes475.0ms (5.6%)

Accuracy

Total 0.1b remaining (78.7%)

Threshold costs 0.1b (78.7%)

Counts

89 → 1

Compiler

Compiled 5396 to 3967 computations (26.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`distribute-rgt-neg-in_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	20	13
2	28	13
3	43	13
4	47	13
5	50	13
6	51	13
7	49	13

end219.0ms (2.6%)

Compiler: Compiled 181 to 128 computations (29.3% 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

analyze179.0ms (2.1%)

sample1.4s (16.9%)

simplify35.0ms (0.4%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series14.0ms (0.2%)

rewrite23.0ms (0.3%)

simplify147.0ms (1.7%)

prune102.0ms (1.2%)

localize8.0ms (0.1%)

series14.0ms (0.2%)

rewrite20.0ms (0.2%)

simplify109.0ms (1.3%)

prune153.0ms (1.8%)

localize17.0ms (0.2%)

series625.0ms (7.3%)

rewrite126.0ms (1.5%)

simplify267.0ms (3.1%)

prune829.0ms (9.7%)

localize20.0ms (0.2%)

series24.0ms (0.3%)

rewrite367.0ms (4.3%)

simplify812.0ms (9.5%)

prune2.5s (29.2%)

regimes475.0ms (5.6%)

simplify4.0ms (0%)

end219.0ms (2.6%)

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