Details

analyze89.0ms (4.1%)

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
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample769.0ms (35.3%)

Results

741.0ms	8256×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	49	11
4	63	11
5	67	11
6	65	11

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
▶	0.2b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 y (.f64 y 3) (.f64 x x))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

simplify61.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
356×	`unswap-sqr_binary64`
323×	`*-commutative_binary64`

Counts

34 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	394
1	35	371
2	66	371
3	184	371
4	793	371
5	3022	371
6	4320	371
7	5097	371

prune18.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	21	3	24
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	21	5	26

Error

0.0b

Counts

26 → 5

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))))
	3.3b	(expm1.f64 (log1p.f64 (fma.f64 y (.f64 y 3) (.f64 x x))))
✓	0.2b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 459 to 237 computations (48.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	0.2b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

series23.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

9.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
7×	`fma-def_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

3 → 51

Calls

3 calls:

6.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
5.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify87.0ms (4%)

Algorithm

1×	egg-herbie

Rules

728×	`fma-neg_binary64`
620×	`fma-def_binary64`
389×	`distribute-rgt-in_binary64`
337×	`distribute-lft-in_binary64`
286×	`unswap-sqr_binary64`

Counts

123 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1464
1	249	1343
2	745	1260
3	3112	1256
4	4528	1256
5	5022	1256

prune72.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	94	5	99

Error

0.0b

Counts

99 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 y (.f64 y 3) (.f64 x x))
	32.2b	(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y)))
	0.9b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y y (.f64 x x))) (cbrt.f64 (fma.f64 y y (.f64 x x)))) (cbrt.f64 (fma.f64 y y (.f64 x x)))) (.f64 y y)) (*.f64 y y))
	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))
▶	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))

Compiler

Compiled 2182 to 493 computations (77.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))

series8.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(fma.f64 3 (*.f64 y y) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 3 (*.f64 y y) (*.f64 x x))

simplify59.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

912×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
356×	`unswap-sqr_binary64`
324×	`*-commutative_binary64`

Counts

34 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	394
1	32	371
2	65	371
3	184	371
4	793	371
5	3022	371
6	4320	371
7	5097	371

prune16.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	23	5	28

Error

0.0b

Counts

28 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 y (.f64 y 3) (.f64 x x))
	32.2b	(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y)))
	0.9b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y y (.f64 x x))) (cbrt.f64 (fma.f64 y y (.f64 x x)))) (cbrt.f64 (fma.f64 y y (.f64 x x)))) (.f64 y y)) (*.f64 y y))
▶	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))

Compiler

Compiled 504 to 203 computations (59.7% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 y (.f64 y 3) (.f64 x x))
✓	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))
✓	6.1b	(sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x)))

series23.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x)))
8.0ms	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))
1.0ms	(sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x)))

simplify83.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

565×	`times-frac_binary64`
429×	`unswap-sqr_binary64`
332×	`associate-l_binary64`
318×	`associate-r_binary64`
250×	`associate-/l*_binary64`

Counts

116 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	2141
1	264	1953
2	830	1863
3	4123	1826
4	5131	1826

prune191.0ms (8.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	222	6	228

Error

Counts

228 → 6

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 y (.f64 y 3) (.f64 x x))
	32.2b	(/.f64 (-.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y)))
	0.5b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))))))
	0.9b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y y (.f64 x x))) (cbrt.f64 (fma.f64 y y (.f64 x x)))) (cbrt.f64 (fma.f64 y y (.f64 x x)))) (.f64 y y)) (*.f64 y y))
✓	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))

Compiler

Compiled 5763 to 3233 computations (43.9% saved)

regimes523.0ms (24%)

Accuracy

Total 0.1b remaining (86.4%)

Threshold costs 0.1b (86.4%)

Counts

95 → 1

Compiler

Compiled 9491 to 5349 computations (43.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	7	11

end80.0ms (3.7%)

Compiler: Compiled 176 to 76 computations (56.8% saved)

Details

analyze89.0ms (4.1%)

sample769.0ms (35.3%)

simplify10.0ms (0.5%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite1.0ms (0%)

simplify61.0ms (2.8%)

prune18.0ms (0.8%)

localize7.0ms (0.3%)

series23.0ms (1.1%)

rewrite16.0ms (0.7%)

simplify87.0ms (4%)

prune72.0ms (3.3%)

localize5.0ms (0.2%)

series8.0ms (0.4%)

rewrite1.0ms (0%)

simplify59.0ms (2.7%)

prune16.0ms (0.7%)

localize7.0ms (0.3%)

series23.0ms (1.1%)

rewrite16.0ms (0.7%)

simplify83.0ms (3.8%)

prune191.0ms (8.8%)

regimes523.0ms (24%)

simplify2.0ms (0.1%)

end80.0ms (3.7%)

Profiling