Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.1s (11.3%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	8
2	16	8
3	17	8
4	17	8

prune4.0ms (0%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 36 to 19 computations (47.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y z) z))
✓	0.1b	(.f64 (.f64 y z) z)

series40.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

25.0ms	(+.f64 x (.f64 (.f64 y z) z))
15.0ms	(.f64 (.f64 y z) z)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 36

Calls

2 calls:

8.0ms	(.f64 (.f64 y z) z)
5.0ms	(+.f64 x (.f64 (.f64 y z) z))

simplify166.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
602×	`fma-neg_binary64`
542×	`distribute-rgt-in_binary64`
454×	`distribute-lft-in_binary64`
284×	`unswap-sqr_binary64`

Counts

96 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	798
1	172	780
2	567	775
3	1235	773
4	2737	773
5	4684	773
6	4942	773

prune64.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Error

0.0b

Counts

58 → 5

Alt Table

Status	Error	Program
	23.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 y z) z)) (sqrt.f64 (.f64 (*.f64 y z) z))))
▶	0.4b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y z) z)) (cbrt.f64 (.f64 (.f64 y z) z))) (cbrt.f64 (.f64 (.f64 y z) z))))
	3.3b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))
	29.8b	(+.f64 x (.f64 (.f64 y (pow.f64 z 3/2)) (sqrt.f64 z)))

Compiler

Compiled 845 to 260 computations (69.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 y z) z)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 y z) z)) (cbrt.f64 (.f64 (.f64 y z) z))) (cbrt.f64 (.f64 (.f64 y z) z)))
✓	0.4b	(.f64 (cbrt.f64 (.f64 (.f64 y z) z)) (cbrt.f64 (.f64 (*.f64 y z) z)))
✓	30.7b	(cbrt.f64 (.f64 (.f64 y z) z))

series2.5s (26.7%)

Counts

3 → 72

Calls

3 calls:

1.4s

(cbrt.f64 (*.f64 (*.f64 y z) z))

1.1s

(*.f64 (cbrt.f64 (*.f64 (*.f64 y z) z)) (cbrt.f64 (*.f64 (*.f64 y z) z)))

44.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y z) z)) (cbrt.f64 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 (*.f64 y z) z)))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

15.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y z) z)) (cbrt.f64 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 (*.f64 y z) z)))

10.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 y z) z)) (cbrt.f64 (*.f64 (*.f64 y z) z)))

5.0ms

(cbrt.f64 (*.f64 (*.f64 y z) z))

simplify209.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

651×	`unswap-sqr_binary64`
407×	`fma-neg_binary64`
356×	`fma-def_binary64`
202×	`exp-prod_binary64`
202×	`log-prod_binary64`

Counts

151 → 130

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	2220
1	278	1992
2	681	1634
3	1466	1454
4	4527	1450
5	4958	1450
6	4975	1450

prune437.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	271	2	273
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	272	6	278

Error

Counts

278 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))
	0.3b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3))
	23.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 y z) z)) (sqrt.f64 (.f64 (*.f64 y z) z))))
	3.3b	(fma.f64 y (*.f64 z z) x)
▶	0.3b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y z)) (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (.f64 y z) z)))) (cbrt.f64 (.f64 (.f64 y z) z))))
	29.8b	(+.f64 x (.f64 (.f64 y (pow.f64 z 3/2)) (sqrt.f64 z)))

Compiler

Compiled 7114 to 1616 computations (77.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 y z)) (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (*.f64 y z) z))))
✓	0.6b	(cbrt.f64 z)
✓	11.6b	(cbrt.f64 (*.f64 y z))
	30.7b	(cbrt.f64 (.f64 (.f64 y z) z))

series2.5s (26.4%)

Counts

3 → 60

Calls

3 calls:

1.4s	(.f64 (cbrt.f64 (.f64 y z)) (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (*.f64 y z) z))))
1.0s	(cbrt.f64 (*.f64 y z))
83.0ms	(cbrt.f64 z)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-exp-log_binary64`
8×	`pow1_binary64`
5×	`pow-prod-down_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

3 → 46

Calls

3 calls:

9.0ms	(.f64 (cbrt.f64 (.f64 y z)) (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (*.f64 y z) z))))
3.0ms	(cbrt.f64 (*.f64 y z))
1.0ms	(cbrt.f64 z)

simplify236.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-neg_binary64`
328×	`fma-def_binary64`
309×	`unswap-sqr_binary64`
264×	`distribute-rgt-in_binary64`
253×	`*-commutative_binary64`

Counts

106 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	124	1587
1	276	1523
2	709	1345
3	1634	1217
4	4399	1169
5	4897	1169
6	4891	1169

prune261.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	139	6	145

Error

Counts

145 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))
▶	0.3b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3))
	23.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 y z) z)) (sqrt.f64 (.f64 (*.f64 y z) z))))
	3.3b	(fma.f64 y (*.f64 z z) x)
✓	0.3b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y z)) (.f64 (cbrt.f64 z) (cbrt.f64 (.f64 (.f64 y z) z)))) (cbrt.f64 (.f64 (.f64 y z) z))))
	29.8b	(+.f64 x (.f64 (.f64 y (pow.f64 z 3/2)) (sqrt.f64 z)))

Compiler

Compiled 3993 to 1050 computations (73.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3))
	0.1b	(.f64 (.f64 y z) z)
✓	0.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3)
	30.7b	(cbrt.f64 (.f64 (.f64 y z) z))

series993.0ms (10.6%)

Counts

2 → 60

Calls

2 calls:

949.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3)
44.0ms	(+.f64 x (pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
4×	`cube-prod_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 45

Calls

2 calls:

12.0ms	(+.f64 x (pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3))
5.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3)

simplify162.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

657×	`fma-neg_binary64`
362×	`unswap-sqr_binary64`
334×	`fma-def_binary64`
300×	`exp-prod_binary64`
279×	`*-commutative_binary64`

Counts

105 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1359
1	275	1302
2	888	1004
3	3043	922
4	4813	922
5	4967	922

prune251.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))
✓	0.3b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 (.f64 y z) z)) 3))
	23.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 y z) z)) (sqrt.f64 (.f64 (*.f64 y z) z))))
	3.4b	(+.f64 x (*.f64 y (pow.f64 (/.f64 -1 z) -2)))

Compiler

Compiled 2035 to 890 computations (56.3% saved)

regimes240.0ms (2.6%)

Accuracy

Total 0.0b remaining (51.8%)

Threshold costs 0.0b (51.8%)

Counts

31 → 1

Compiler

Compiled 2520 to 1425 computations (43.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end97.0ms (1%)

Compiler: Compiled 73 to 44 computations (39.7% saved)

Details

analyze3.0ms (0%)

sample1.1s (11.3%)

simplify14.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series40.0ms (0.4%)

rewrite16.0ms (0.2%)

simplify166.0ms (1.8%)

prune64.0ms (0.7%)

localize17.0ms (0.2%)

series2.5s (26.7%)

rewrite40.0ms (0.4%)

simplify209.0ms (2.2%)

prune437.0ms (4.7%)

localize18.0ms (0.2%)

series2.5s (26.4%)

rewrite16.0ms (0.2%)

simplify236.0ms (2.5%)

prune261.0ms (2.8%)

localize16.0ms (0.2%)

series993.0ms (10.6%)

rewrite20.0ms (0.2%)

simplify162.0ms (1.7%)

prune251.0ms (2.7%)

regimes240.0ms (2.6%)

simplify3.0ms (0%)

end97.0ms (1%)

Profiling