Details

analyze3.0ms (0.2%)

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)

sample730.0ms (36.6%)

Results

701.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify6.0ms (0.3%)

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

prune3.0ms (0.2%)

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 (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite5.0ms (0.2%)

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)

simplify63.0ms (3.2%)

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

prune22.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 3 (pow.f64 x 2))
✓	0.2b	(.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)))
	23.5b	(cbrt.f64 (*.f64 27 (pow.f64 x 6)))
	23.5b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x 3) x) (.f64 (.f64 x 3) x)) (.f64 (.f64 x 3) x)))

Compiler

Compiled 406 to 262 computations (35.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

2.0ms

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

rewrite6.0ms (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))

simplify91.0ms (4.6%)

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

prune34.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	43	7	50

Error

0.0b

Counts

50 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (sqrt.f64 3) (.f64 x (*.f64 x (sqrt.f64 3))))
✓	0.2b	(.f64 (.f64 x 3) x)
✓	0.2b	(*.f64 3 (pow.f64 x 2))
	0.5b	(.f64 (.f64 3 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2)))
	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)))
	23.5b	(cbrt.f64 (*.f64 27 (pow.f64 x 6)))
	23.5b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x 3) x) (.f64 (.f64 x 3) x)) (.f64 (.f64 x 3) x)))

Compiler

Compiled 610 to 462 computations (24.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series15.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 3) (.f64 x (*.f64 x (sqrt.f64 3))))
4.0ms	(.f64 x (.f64 x (sqrt.f64 3)))
3.0ms	(*.f64 x (sqrt.f64 3))

rewrite18.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`

Counts

3 → 70

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 3) (.f64 x (*.f64 x (sqrt.f64 3))))
4.0ms	(.f64 x (.f64 x (sqrt.f64 3)))
3.0ms	(*.f64 x (sqrt.f64 3))

simplify73.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
683×	`associate-/r/_binary64`
343×	`*-commutative_binary64`
251×	`sqr-pow_binary64`
205×	`times-frac_binary64`

Counts

106 → 99

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	81	1028
1	175	920
2	590	908
3	857	898
4	1499	895
5	2543	895
6	5072	895

prune78.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	100	6	106

Error

Counts

106 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 3) (.f64 x (.f64 (.f64 x (fabs.f64 (cbrt.f64 3))) (sqrt.f64 (cbrt.f64 3)))))
✓	0.2b	(*.f64 3 (pow.f64 x 2))
	0.5b	(.f64 (.f64 3 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (pow.f64 x 2)))
▶	0.3b	(.f64 (sqrt.f64 3) (.f64 x (.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))) (cbrt.f64 (sqrt.f64 3)))))
✓	0.2b	(.f64 (.f64 x 3) x)
	23.5b	(cbrt.f64 (*.f64 27 (pow.f64 x 6)))

Compiler

Compiled 1490 to 1143 computations (23.3% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 3) (.f64 x (.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))) (cbrt.f64 (sqrt.f64 3)))))
✓	0.3b	(.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))) (cbrt.f64 (sqrt.f64 3)))
✓	0.4b	(.f64 x (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))))
✓	1.0b	(*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))

series349.0ms (17.5%)

Counts

4 → 36

Calls

4 calls:

339.0ms	(.f64 x (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))))
7.0ms	(.f64 (sqrt.f64 3) (.f64 x (.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))) (cbrt.f64 (sqrt.f64 3)))))
3.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))) (cbrt.f64 (sqrt.f64 3)))
0.0ms	(*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))

rewrite45.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`cbrt-prod_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`pow1_binary64`
40×	`add-exp-log_binary64`
26×	`sqrt-prod_binary64`

Counts

4 → 140

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 3) (.f64 x (.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))) (cbrt.f64 (sqrt.f64 3)))))
8.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))) (cbrt.f64 (sqrt.f64 3)))
8.0ms	(*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))
6.0ms	(.f64 x (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))))

simplify128.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

763×	`fma-def_binary64`
504×	`sqr-pow_binary64`
495×	`*-commutative_binary64`
348×	`swap-sqr_binary64`
325×	`exp-prod_binary64`

Counts

176 → 176

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	146	2374
1	306	1906
2	1084	1780
3	2086	1714
4	3518	1489
5	4936	1489
6	5094	1489

prune164.0ms (8.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	177	5	182

Error

Counts

182 → 5

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 3 (pow.f64 x 2))
	0.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (.f64 x x) (pow.f64 (cbrt.f64 (sqrt.f64 3)) 4)))
✓	0.3b	(.f64 (sqrt.f64 3) (.f64 x (.f64 (.f64 x (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))) (cbrt.f64 (sqrt.f64 3)))))
✓	0.2b	(.f64 (.f64 x 3) x)
	23.5b	(cbrt.f64 (*.f64 27 (pow.f64 x 6)))

Compiler

Compiled 4012 to 3533 computations (11.9% saved)

regimes65.0ms (3.3%)

Accuracy

Total 0.2b remaining (89%)

Threshold costs 0.2b (89%)

Counts

36 → 1

Compiler

Compiled 970 to 800 computations (17.5% 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

end71.0ms (3.5%)

Compiler: Compiled 68 to 56 computations (17.6% saved)

Details

analyze3.0ms (0.2%)

sample730.0ms (36.6%)

simplify6.0ms (0.3%)

prune3.0ms (0.2%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify63.0ms (3.2%)

prune22.0ms (1.1%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite6.0ms (0.3%)

simplify91.0ms (4.6%)

prune34.0ms (1.7%)

localize6.0ms (0.3%)

series15.0ms (0.7%)

rewrite18.0ms (0.9%)

simplify73.0ms (3.7%)

prune78.0ms (3.9%)

localize8.0ms (0.4%)

series349.0ms (17.5%)

rewrite45.0ms (2.3%)

simplify128.0ms (6.4%)

prune164.0ms (8.2%)

regimes65.0ms (3.3%)

simplify2.0ms (0.1%)

end71.0ms (3.5%)

Profiling