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)

sample525.0ms (20.9%)

Infinites

24.6% of outputs are infinite.

Results

460.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify18.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-def_binary64`
84×	`fma-neg_binary64`
35×	`distribute-rgt-in_binary64`
26×	`unsub-neg_binary64`
25×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

prune1.0ms (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 x (-.f64 1 (.f64 x 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 x (-.f64 1 (.f64 x y)))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`prod-diff_binary64`
5×	`distribute-lft-in_binary64`
5×	`distribute-rgt-in_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 32

Calls

1 calls:

5.0ms

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

simplify60.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
584×	`unsub-neg_binary64`
561×	`distribute-neg-out_binary64`
311×	`associate-l_binary64`
293×	`unswap-sqr_binary64`

Counts

56 → 51

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	723
1	140	663
2	421	626
3	1318	606
4	2818	606
5	5568	606

prune43.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Error

0.0b

Counts

52 → 7

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
	6.9b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	16.1b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
	25.6b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	23.2b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
▶	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
	9.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))

Compiler

Compiled 962 to 457 computations (52.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(.f64 (neg.f64 (.f64 x y)) x)
9.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-l_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(.f64 (neg.f64 (.f64 x y)) x)
3.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

simplify98.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

786×	`unsub-neg_binary64`
423×	`times-frac_binary64`
380×	`neg-sub0_binary64`
365×	`neg-mul-1_binary64`
320×	`distribute-lft-neg-out_binary64`

Counts

88 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	933
1	189	909
2	748	899
3	2086	893
4	3687	893
5	4607	893
6	5301	893

prune62.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	70	7	77

Error

Counts

77 → 7

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
	6.9b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	16.1b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
	25.6b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	29.6b	(+.f64 (.f64 1 x) (.f64 (*.f64 y (neg.f64 (pow.f64 x 3/2))) (sqrt.f64 x)))
✓	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
	9.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))

Compiler

Compiled 1284 to 530 computations (58.7% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
✓	14.7b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))

series86.0ms (3.4%)

Counts

3 → 72

Calls

3 calls:

40.0ms

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

30.0ms

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

16.0ms

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

rewrite33.0ms (1.3%)

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:

8.0ms

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

5.0ms

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

3.0ms

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

simplify141.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

734×	`cancel-sign-sub-inv_binary64`
304×	`associate-/r*_binary64`
208×	`associate-l_binary64`
192×	`sub-neg_binary64`
192×	`times-frac_binary64`

Counts

187 → 247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	6638
1	922	6109
2	3303	5782
3	5086	5782

prune539.0ms (21.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	524	0	524
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	524	7	531

Error

Counts

531 → 7

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
▶	6.9b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	16.1b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
	25.6b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	29.6b	(+.f64 (.f64 1 x) (.f64 (*.f64 y (neg.f64 (pow.f64 x 3/2))) (sqrt.f64 x)))
✓	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
	9.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))

Compiler

Compiled 21625 to 11956 computations (44.7% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	8.3b	(*.f64 y (pow.f64 x 2))

series96.0ms (3.8%)

Counts

2 → 6

Calls

2 calls:

81.0ms	(-.f64 x (*.f64 y (pow.f64 x 2)))
15.0ms	(*.f64 y (pow.f64 x 2))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`

Counts

2 → 49

Calls

2 calls:

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

simplify118.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

518×	`fma-neg_binary64`
448×	`associate-l_binary64`
412×	`unswap-sqr_binary64`
398×	`associate-r_binary64`
375×	`distribute-rgt-neg-in_binary64`

Counts

55 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	730
1	176	586
2	495	558
3	2159	558
4	4134	558
5	4989	558
6	4819	558

prune131.0ms (5.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	82	7	89

Error

Counts

89 → 7

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	6.9b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	16.1b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
	25.6b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	29.6b	(+.f64 (.f64 1 x) (.f64 (*.f64 y (neg.f64 (pow.f64 x 3/2))) (sqrt.f64 x)))
✓	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
	9.6b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))

Compiler

Compiled 1181 to 607 computations (48.6% saved)

regimes329.0ms (13.1%)

Accuracy

Total 0.1b remaining (83.9%)

Threshold costs 0.1b (83.9%)

Counts

62 → 1

Compiler

Compiled 3360 to 2073 computations (38.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	26	10
3	37	10
4	43	10
5	46	10
6	47	10
7	46	10

end145.0ms (5.8%)

Compiler: Compiled 137 to 86 computations (37.2% saved)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Details

analyze1.0ms (0%)

sample525.0ms (20.9%)

simplify18.0ms (0.7%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite7.0ms (0.3%)

simplify60.0ms (2.4%)

prune43.0ms (1.7%)

localize6.0ms (0.2%)

series19.0ms (0.7%)

rewrite7.0ms (0.3%)

simplify98.0ms (3.9%)

prune62.0ms (2.5%)

localize8.0ms (0.3%)

series86.0ms (3.4%)

rewrite33.0ms (1.3%)

simplify141.0ms (5.6%)

prune539.0ms (21.5%)

localize9.0ms (0.4%)

series96.0ms (3.8%)

rewrite16.0ms (0.6%)

simplify118.0ms (4.7%)

prune131.0ms (5.2%)

regimes329.0ms (13.1%)

simplify5.0ms (0.2%)

end145.0ms (5.8%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10