Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 10 to 7 computations (30% saved)

sample550.0ms (14%)

Infinites

25.1% of outputs are infinite.

Results

468.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify24.0ms (0.6%)

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))

series8.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.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))

simplify109.0ms (2.8%)

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

prune87.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	6	74

Error

Counts

74 → 6

Alt Table

Status	Error	Program
	35.9b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	14.3b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
▶	0.4b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
	3.7b	(.f64 x (.f64 y (-.f64 1 y)))

Compiler

Compiled 1460 to 640 computations (56.2% saved)

localize8.0ms (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 1 y)))
✓	0.1b	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
✓	0.3b	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
✓	0.3b	(cbrt.f64 (-.f64 1 y))

series400.0ms (10.2%)

Counts

4 → 72

Calls

4 calls:

380.0ms	(.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)))
7.0ms	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
5.0ms	(cbrt.f64 (-.f64 1 y))

rewrite65.0ms (1.7%)

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:

19.0ms	(.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))))
11.0ms	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
2.0ms	(cbrt.f64 (-.f64 1 y))

simplify155.0ms (4%)

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	4491
4	4984	4491

prune373.0ms (9.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	376	0	376
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	376	6	382

Error

Counts

382 → 6

Alt Table

Status	Error	Program
	35.9b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
▶	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	14.3b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.4b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
	3.7b	(.f64 x (.f64 y (-.f64 1 y)))

Compiler

Compiled 10643 to 7456 computations (29.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (*.f64 x y) (-.f64 1 y))))
✓	20.8b	(cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))

series922.0ms (23.5%)

Counts

3 → 72

Calls

3 calls:

562.0ms

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

329.0ms

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

30.0ms

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

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

11.0ms

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

6.0ms

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

4.0ms

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

simplify163.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-def_binary64`
601×	`times-frac_binary64`
297×	`cancel-sign-sub-inv_binary64`
296×	`fma-neg_binary64`
231×	`associate-l_binary64`

Counts

187 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	288	5751
1	693	5324
2	2213	4690
3	4848	4688
4	4959	4688

prune488.0ms (12.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	553	0	553
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	553	6	559

Error

Counts

559 → 6

Alt Table

Status	Error	Program
	35.9b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
✓	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	14.3b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.4b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
▶	3.7b	(.f64 x (.f64 y (-.f64 1 y)))

Compiler

Compiled 21034 to 11625 computations (44.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 1 y))
✓	3.7b	(.f64 x (.f64 y (-.f64 1 y)))

series10.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

7.0ms	(.f64 x (.f64 y (-.f64 1 y)))
2.0ms	(*.f64 y (-.f64 1 y))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
52×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`

Counts

2 → 125

Calls

2 calls:

8.0ms	(.f64 x (.f64 y (-.f64 1 y)))
6.0ms	(*.f64 y (-.f64 1 y))

simplify110.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

468×	`*-commutative_binary64`
386×	`exp-prod_binary64`
367×	`fma-def_binary64`
307×	`distribute-rgt-neg-out_binary64`
294×	`distribute-lft-neg-out_binary64`

Counts

161 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2288
1	243	2085
2	1064	1753
3	2742	1585
4	4514	1585
5	4766	1585

prune119.0ms (3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	165	6	171

Error

Counts

171 → 6

Alt Table

Status	Error	Program
	35.9b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
✓	0.8b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	14.3b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.4b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
✓	3.7b	(.f64 x (.f64 y (-.f64 1 y)))

Compiler

Compiled 3189 to 1352 computations (57.6% saved)

regimes162.0ms (4.1%)

Accuracy

Total 0.1b remaining (80.1%)

Threshold costs 0.1b (80.1%)

Counts

58 → 1

Compiler

Compiled 3138 to 2165 computations (31% 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

end77.0ms (2%)

Compiler: Compiled 113 to 77 computations (31.9% 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

analyze1.0ms (0%)

sample550.0ms (14%)

simplify24.0ms (0.6%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite11.0ms (0.3%)

simplify109.0ms (2.8%)

prune87.0ms (2.2%)

localize8.0ms (0.2%)

series400.0ms (10.2%)

rewrite65.0ms (1.7%)

simplify155.0ms (4%)

prune373.0ms (9.5%)

localize8.0ms (0.2%)

series922.0ms (23.5%)

rewrite36.0ms (0.9%)

simplify163.0ms (4.1%)

prune488.0ms (12.4%)

localize5.0ms (0.1%)

series10.0ms (0.2%)

rewrite27.0ms (0.7%)

simplify110.0ms (2.8%)

prune119.0ms (3%)

regimes162.0ms (4.1%)

simplify2.0ms (0.1%)

end77.0ms (2%)

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