Details

analyze88.0ms (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)

sample826.0ms (26.8%)

Results

747.0ms	8256×	body	128	valid
14.0ms	185×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify25.0ms (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

prune2.0ms (0.1%)

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)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite12.0ms (0.4%)

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:

9.0ms

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

simplify101.0ms (3.3%)

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

prune52.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Error

0.0b

Counts

74 → 5

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y)))
	31.1b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
	28.0b	(.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (sqrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))
▶	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	7.0b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 1425 to 606 computations (57.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 y) x)
✓	0.1b	(.f64 y (.f64 (-.f64 1 y) x))

series10.0ms (0.3%)

Counts

2 → 28

Calls

2 calls:

6.0ms	(.f64 y (.f64 (-.f64 1 y) x))
4.0ms	(*.f64 (-.f64 1 y) x)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`associate-l_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

6.0ms	(.f64 y (.f64 (-.f64 1 y) x))
4.0ms	(*.f64 (-.f64 1 y) x)

simplify55.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
371×	`unsub-neg_binary64`
324×	`unswap-sqr_binary64`
288×	`*-commutative_binary64`
245×	`associate-+l+_binary64`

Counts

75 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	819
1	186	726
2	553	723
3	1335	720
4	2735	720
5	4950	720

prune51.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	81	5	86

Error

0.0b

Counts

86 → 5

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y)))
	31.1b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
	28.0b	(.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (sqrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))
✓	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	7.0b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 1133 to 597 computations (47.3% saved)

localize13.0ms (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))
✓	0.3b	(.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)

series107.0ms (3.5%)

Counts

4 → 60

Calls

4 calls:

35.0ms	(cbrt.f64 y)
34.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
23.0ms	(.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y))
14.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))

rewrite20.0ms (0.6%)

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:

6.0ms	(.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (.f64 x y))
5.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify124.0ms (4%)

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	1341
2	1151	1286
3	2648	1258
4	4095	1246
5	4890	1246
6	4929	1246

prune155.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	196	6	202

Error

0.0b

Counts

202 → 6

Alt Table

Status	Error	Program
	31.1b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
▶	0.6b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)))) (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))))) (cbrt.f64 y)) (.f64 x y)))
	33.3b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (sqrt.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))) (sqrt.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)))) (*.f64 x y)))
	28.0b	(.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (sqrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))
✓	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	7.0b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 4818 to 1659 computations (65.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series581.0ms (18.9%)

Counts

2 → 24

Calls

2 calls:

297.0ms	(.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))))
284.0ms	(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`cbrt-prod_binary64`
9×	`pow1_binary64`
7×	`pow1/3_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 47

Calls

2 calls:

4.0ms	(.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))))
2.0ms	(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))

simplify85.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

517×	`associate-*r/_binary64`
457×	`associate-*l/_binary64`
298×	`sqr-pow_binary64`
293×	`unswap-sqr_binary64`
288×	`swap-sqr_binary64`

Counts

71 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	1134
1	110	1066
2	262	973
3	766	955
4	1459	771
5	2110	771
6	4470	771
7	4886	771

prune430.0ms (14%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	428	1	429
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	428	7	435

Error

Counts

435 → 7

Alt Table

Status	Error	Program
	31.1b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
✓	0.6b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)))) (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))))) (cbrt.f64 y)) (.f64 x y)))
	33.3b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (sqrt.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))) (sqrt.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)))) (*.f64 x y)))
	2.2b	(+.f64 (.f64 1 (.f64 x y)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (cbrt.f64 y)))) (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))))) (cbrt.f64 y)) (.f64 x y)))
	28.0b	(.f64 (sqrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (sqrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))
✓	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	7.0b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 16529 to 4647 computations (71.9% saved)

regimes208.0ms (6.8%)

Accuracy

Total 0.1b remaining (72.9%)

Threshold costs 0.1b (72.9%)

Counts

57 → 1

Compiler

Compiled 3971 to 2182 computations (45.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	17	10
3	19	10
4	20	10
5	19	10

end84.0ms (2.7%)

Compiler: Compiled 174 to 88 computations (49.4% 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

analyze88.0ms (2.8%)

sample826.0ms (26.8%)

simplify25.0ms (0.8%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series7.0ms (0.2%)

rewrite12.0ms (0.4%)

simplify101.0ms (3.3%)

prune52.0ms (1.7%)

localize4.0ms (0.1%)

series10.0ms (0.3%)

rewrite12.0ms (0.4%)

simplify55.0ms (1.8%)

prune51.0ms (1.6%)

localize13.0ms (0.4%)

series107.0ms (3.5%)

rewrite20.0ms (0.6%)

simplify124.0ms (4%)

prune155.0ms (5%)

localize13.0ms (0.4%)

series581.0ms (18.9%)

rewrite8.0ms (0.3%)

simplify85.0ms (2.8%)

prune430.0ms (14%)

regimes208.0ms (6.8%)

simplify2.0ms (0.1%)

end84.0ms (2.7%)

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