Details

analyze6.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample626.0ms (40.4%)

Results

599.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify16.0ms (1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-l_binary64`
1×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	10	7
3	10	7

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.2b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 23 to 15 computations (34.8% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (*.f64 x 3) x)

rewrite4.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (*.f64 x 3) x)

simplify64.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
445×	`times-frac_binary64`
424×	`distribute-rgt-in_binary64`
318×	`associate-l_binary64`
257×	`sqr-pow_binary64`

Counts

32 → 31

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	296
1	89	260
2	280	251
3	551	249
4	764	249
5	1314	249
6	2592	249
7	4883	249
8	4953	249

prune24.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	26	5	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	6	32

Error

0.0b

Counts

32 → 6

Alt Table

Status	Error	Program
	34.3b	(.f64 (.f64 3 (pow.f64 x 3/2)) (sqrt.f64 x))
	1.0b	(.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
	0.3b	(.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (*.f64 x 3) x)))
	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x 3) x)) (cbrt.f64 (.f64 (.f64 x 3) x))) (cbrt.f64 (.f64 (.f64 x 3) x)))
▶	0.2b	(*.f64 3 (pow.f64 x 2))
✓	0.2b	(.f64 (.f64 x 3) x)

Compiler

Compiled 426 to 272 computations (36.2% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 3 (pow.f64 x 2))

series3.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 3 (pow.f64 x 2))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

4.0ms

(*.f64 3 (pow.f64 x 2))

simplify93.0ms (6%)

Algorithm

1×	egg-herbie

Rules

656×	`unswap-sqr_binary64`
445×	`exp-prod_binary64`
443×	`log-prod_binary64`
398×	`cube-prod_binary64`
337×	`*-commutative_binary64`

Counts

29 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	321
1	97	249
2	197	239
3	636	233
4	1074	233
5	2909	233
6	3983	233
7	4567	233
8	4972	233
9	4879	233

prune43.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	44	7	51

Error

0.0b

Counts

51 → 7

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 3 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2)))
✓	0.2b	(.f64 (.f64 x 3) x)
	34.3b	(.f64 (.f64 3 (pow.f64 x 3/2)) (sqrt.f64 x))
	0.4b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))
▶	0.3b	(.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (*.f64 x 3) x)))
	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x 3) x)) (cbrt.f64 (.f64 (.f64 x 3) x))) (cbrt.f64 (.f64 (.f64 x 3) x)))
✓	0.2b	(*.f64 3 (pow.f64 x 2))

Compiler

Compiled 610 to 466 computations (23.6% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 x 3) x)
✓	0.3b	(.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (*.f64 x 3) x)))
✓	19.3b	(sqrt.f64 (.f64 (.f64 x 3) x))

series10.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (*.f64 x 3) x)))
3.0ms	(sqrt.f64 (.f64 (.f64 x 3) x))

rewrite19.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

135×	`pow1_binary64`
74×	`pow-prod-down_binary64`
63×	`sqrt-pow1_binary64`
17×	`pow-prod-up_binary64`
13×	`pow1/2_binary64`

Counts

2 → 82

Calls

2 calls:

10.0ms	(.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (*.f64 x 3) x)))
2.0ms	(sqrt.f64 (.f64 (.f64 x 3) x))

simplify88.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-l_binary64`
589×	`fma-def_binary64`
509×	`sqr-pow_binary64`
437×	`associate-r_binary64`
299×	`swap-sqr_binary64`

Counts

106 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	957
1	98	797
2	322	747
3	1763	642
4	2226	584
5	3697	584
6	5027	584

prune133.0ms (8.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	166	8	174

Error

Counts

174 → 8

Alt Table

Status	Error	Program
	18.9b	(sqrt.f64 (*.f64 9 (pow.f64 x 4)))
	0.9b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x 3) x)) (cbrt.f64 (.f64 (.f64 x 3) x))) (cbrt.f64 (.f64 (.f64 x 3) x)))
	0.9b	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 x 3) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 x 3) x))))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 x 3) x))))
▶	0.4b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))
	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 x 3) x))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 x 3) x))) (sqrt.f64 (.f64 (.f64 x 3) x))))
✓	0.3b	(.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (*.f64 x 3) x)))
✓	0.2b	(*.f64 3 (pow.f64 x 2))
	0.6b	(.f64 (.f64 3 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2)))

Compiler

Compiled 2937 to 2089 computations (28.9% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))
✓	0.3b	(*.f64 (cbrt.f64 3) (pow.f64 x 2))

series19.0ms (1.2%)

Counts

2 → 12

Calls

2 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))
5.0ms	(*.f64 (cbrt.f64 3) (pow.f64 x 2))

rewrite15.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
21×	`prod-exp_binary64`
18×	`add-sqr-sqrt_binary64`
9×	`associate-r_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 62

Calls

2 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (pow.f64 x 2)))
5.0ms	(*.f64 (cbrt.f64 3) (pow.f64 x 2))

simplify87.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

527×	`times-frac_binary64`
398×	`unswap-sqr_binary64`
392×	`fma-def_binary64`
321×	`log-prod_binary64`
302×	`associate-+l+_binary64`

Counts

74 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	929
1	165	724
2	489	714
3	811	693
4	1373	693
5	3632	693
6	4363	693
7	4969	693

prune102.0ms (6.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	3	2	5
Picked	1	0	1
Done	0	2	2
Total	91	6	97

Error

Counts

97 → 6

Alt Table

Status	Error	Program
	0.9b	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 x 3) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 x 3) x))))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 x 3) x))))
	0.4b	(.f64 (cbrt.f64 3) (.f64 (.f64 x x) (.f64 (cbrt.f64 3) (cbrt.f64 3))))
✓	0.3b	(.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (*.f64 x 3) x)))
✓	0.2b	(*.f64 3 (pow.f64 x 2))
	0.3b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 x (*.f64 x (cbrt.f64 (sqrt.f64 3))))))
	0.6b	(.f64 (.f64 3 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2)))

Compiler

Compiled 1622 to 1396 computations (13.9% saved)

regimes81.0ms (5.3%)

Accuracy

Total 0.2b remaining (90.8%)

Threshold costs 0.2b (90.8%)

Counts

46 → 1

Compiler

Compiled 1322 to 1084 computations (18% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	7	7

end85.0ms (5.5%)

Compiler: Compiled 106 to 82 computations (22.6% saved)

Details

analyze6.0ms (0.4%)

sample626.0ms (40.4%)

simplify16.0ms (1%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite4.0ms (0.3%)

simplify64.0ms (4.2%)

prune24.0ms (1.6%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite5.0ms (0.3%)

simplify93.0ms (6%)

prune43.0ms (2.8%)

localize5.0ms (0.3%)

series10.0ms (0.7%)

rewrite19.0ms (1.3%)

simplify88.0ms (5.7%)

prune133.0ms (8.6%)

localize6.0ms (0.4%)

series19.0ms (1.2%)

rewrite15.0ms (1%)

simplify87.0ms (5.6%)

prune102.0ms (6.6%)

regimes81.0ms (5.3%)

simplify2.0ms (0.1%)

end85.0ms (5.5%)

Profiling