Details

analyze2.0ms (0.1%)

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)

sample894.0ms (22.3%)

Results

803.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify33.0ms (0.8%)

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

prune3.0ms (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)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite8.0ms (0.2%)

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:

6.0ms

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

simplify91.0ms (2.3%)

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

prune44.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	42	9	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	9	52

Error

Counts

52 → 9

Alt Table

Status	Error	Program
	29.5b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	26.8b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
	4.9b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	14.8b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
▶	0.4b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	30.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	25.0b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	11.6b	(+.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 992 to 477 computations (51.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
✓	0.3b	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
✓	8.1b	(cbrt.f64 (-.f64 1 (*.f64 x y)))

series131.0ms (3.3%)

Counts

4 → 96

Calls

4 calls:

43.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
40.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
32.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))
15.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))

rewrite84.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
40×	`flip--_binary64`
40×	`flip3--_binary64`
36×	`frac-times_binary64`

Counts

4 → 146

Calls

4 calls:

24.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
15.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
8.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
2.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))

simplify328.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

373×	`associate-l_binary64`
328×	`distribute-neg-frac_binary64`
325×	`associate-r_binary64`
324×	`associate-/r*_binary64`
268×	`sub-neg_binary64`

Counts

242 → 334

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	8447
1	1100	7636
2	3705	7166
3	5208	7166

prune838.0ms (20.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	464	0	464
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	464	9	473

Error

Counts

473 → 9

Alt Table

Status	Error	Program
	29.5b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	26.8b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
	4.9b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	14.8b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
✓	0.4b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	30.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
▶	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	25.0b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	11.6b	(+.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 18596 to 10856 computations (41.6% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
✓	0.4b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series282.0ms (7.1%)

Counts

4 → 72

Calls

4 calls:

125.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
68.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
58.0ms	(cbrt.f64 x)
31.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`

Counts

4 → 137

Calls

4 calls:

15.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
9.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
8.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify237.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

500×	`exp-prod_binary64`
419×	`fma-neg_binary64`
398×	`fma-def_binary64`
345×	`associate-l_binary64`
291×	`distribute-rgt-in_binary64`

Counts

209 → 195

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	2627
1	348	2339
2	1356	2193
3	3351	2063
4	4202	1965
5	4737	1965
6	4598	1965

prune180.0ms (4.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	231	9	240

Error

Counts

240 → 9

Alt Table

Status	Error	Program
	29.5b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	26.8b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
▶	4.9b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	14.8b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
✓	0.4b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	30.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
✓	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	25.0b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	11.6b	(+.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 4874 to 1798 computations (63.1% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	6.4b	(*.f64 y (pow.f64 x 2))

series21.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(-.f64 x (*.f64 y (pow.f64 x 2)))
9.0ms	(*.f64 y (pow.f64 x 2))

rewrite17.0ms (0.4%)

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:

9.0ms	(*.f64 y (pow.f64 x 2))
5.0ms	(-.f64 x (*.f64 y (pow.f64 x 2)))

simplify139.0ms (3.5%)

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

prune101.0ms (2.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	82	9	91

Error

Counts

91 → 9

Alt Table

Status	Error	Program
	29.5b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	26.8b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
✓	4.9b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	14.8b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
✓	0.4b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	30.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
✓	1.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	25.0b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	11.6b	(+.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 1210 to 623 computations (48.5% saved)

regimes245.0ms (6.1%)

Accuracy

Total 0.1b remaining (81.7%)

Threshold costs 0.1b (81.7%)

Counts

51 → 1

Compiler

Compiled 2350 to 1514 computations (35.6% saved)

simplify5.0ms (0.1%)

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	10	10
1	19	10
2	33	10
3	41	10
4	47	10
5	49	10
6	47	10

end222.0ms (5.6%)

Compiler: Compiled 166 to 102 computations (38.6% 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

analyze2.0ms (0.1%)

sample894.0ms (22.3%)

simplify33.0ms (0.8%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series7.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify91.0ms (2.3%)

prune44.0ms (1.1%)

localize10.0ms (0.3%)

series131.0ms (3.3%)

rewrite84.0ms (2.1%)

simplify328.0ms (8.2%)

prune838.0ms (20.9%)

localize16.0ms (0.4%)

series282.0ms (7.1%)

rewrite49.0ms (1.2%)

simplify237.0ms (5.9%)

prune180.0ms (4.5%)

localize4.0ms (0.1%)

series21.0ms (0.5%)

rewrite17.0ms (0.4%)

simplify139.0ms (3.5%)

prune101.0ms (2.5%)

regimes245.0ms (6.1%)

simplify5.0ms (0.1%)

end222.0ms (5.6%)

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