Details

analyze2.0ms (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)

sample635.0ms (16.6%)

Infinites

25.1% of outputs are infinite.

Results

591.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify9.0ms (0.2%)

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

prune2.0ms (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
	0.1b	(fma.f64 z (*.f64 y z) x)
▶	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 54 to 29 computations (46.3% saved)

localize4.0ms (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)

series20.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

11.0ms	(+.f64 x (.f64 (.f64 y z) z))
8.0ms	(.f64 (.f64 y z) z)

rewrite12.0ms (0.3%)

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:

4.0ms	(.f64 (.f64 y z) z)
2.0ms	(+.f64 x (.f64 (.f64 y z) z))

simplify95.0ms (2.5%)

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

prune223.0ms (5.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	54	5	59

Error

0.0b

Counts

59 → 5

Alt Table

Status	Error	Program
	31.5b	(+.f64 x (.f64 (.f64 (*.f64 y z) (sqrt.f64 z)) (sqrt.f64 z)))
	20.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 y z) z)) (sqrt.f64 (.f64 (*.f64 y z) z))))
	2.8b	(fma.f64 y (*.f64 z z) x)
▶	0.1b	(fma.f64 z (*.f64 y z) x)
	1.0b	(.f64 (.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))) (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))

Compiler

Compiled 863 to 262 computations (69.6% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

11.0ms

(fma.f64 z (*.f64 y z) 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:

1.0ms

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

simplify102.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

557×	`fma-def_binary64`
534×	`unswap-sqr_binary64`
444×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	382
1	32	365
2	56	365
3	152	365
4	615	365
5	2186	365
6	2764	365
7	4969	365
8	5049	365

prune29.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	23	5	28

Error

0.0b

Counts

28 → 5

Alt Table

Status	Error	Program
	31.5b	(+.f64 x (.f64 (.f64 (*.f64 y z) (sqrt.f64 z)) (sqrt.f64 z)))
	20.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 y z) z)) (sqrt.f64 (.f64 (*.f64 y z) z))))
	2.8b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(fma.f64 z (*.f64 y z) x)
▶	1.0b	(.f64 (.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))) (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))

Compiler

Compiled 376 to 119 computations (68.4% saved)

localize14.0ms (0.4%)

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 x (.f64 (.f64 y z) z))) (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))
✓	0.5b	(.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))) (cbrt.f64 (+.f64 x (.f64 (*.f64 y z) z))))
✓	16.1b	(cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))

series215.0ms (5.6%)

Counts

3 → 108

Calls

3 calls:

100.0ms

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

96.0ms

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

18.0ms

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

rewrite99.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
32×	`frac-times_binary64`
29×	`pow1_binary64`

Counts

3 → 129

Calls

3 calls:

54.0ms

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

14.0ms

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

3.0ms

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

simplify265.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

407×	`associate-r_binary64`
362×	`unswap-sqr_binary64`
350×	`associate-l_binary64`
293×	`times-frac_binary64`
272×	`associate-/r*_binary64`

Counts

237 → 290

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	423	8914
1	1222	8343
2	4193	7932
3	5323	7932

prune396.0ms (10.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	534	1	535
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	535	5	540

Error

Counts

540 → 5

Alt Table

Status	Error	Program
	31.5b	(+.f64 x (.f64 (.f64 (*.f64 y z) (sqrt.f64 z)) (sqrt.f64 z)))
	20.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 y z) z)) (sqrt.f64 (.f64 (*.f64 y z) z))))
	2.8b	(fma.f64 y (*.f64 z z) x)
▶	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))) (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))) (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))))
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 23898 to 7742 computations (67.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))) (cbrt.f64 (+.f64 x (.f64 (*.f64 y z) z))))
✓	0.5b	(.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (*.f64 y z) z)))))
✓	0.5b	(cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))
	16.1b	(cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))

series168.0ms (4.4%)

Counts

2 → 72

Calls

2 calls:

104.0ms	(.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (*.f64 y z) z)))))
63.0ms	(cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
28×	`cbrt-div_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

2 → 82

Calls

2 calls:

9.0ms	(.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (*.f64 y z) z)))))
2.0ms	(cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))

simplify156.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

361×	`associate-r_binary64`
337×	`unswap-sqr_binary64`
293×	`times-frac_binary64`
280×	`associate-/r*_binary64`
254×	`associate-l_binary64`

Counts

154 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	421	7556
1	1210	6782
2	4071	6459
3	5130	6459

prune1.1s (27.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	896	0	896
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	896	5	901

Error

Counts

901 → 5

Alt Table

Status	Error	Program
	31.5b	(+.f64 x (.f64 (.f64 (*.f64 y z) (sqrt.f64 z)) (sqrt.f64 z)))
	20.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 y z) z)) (sqrt.f64 (.f64 (*.f64 y z) z))))
	2.8b	(fma.f64 y (*.f64 z z) x)
✓	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))) (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z)))) (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))) (cbrt.f64 (cbrt.f64 (+.f64 x (.f64 (.f64 y z) z))))))
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 62330 to 18080 computations (71% saved)

regimes217.0ms (5.7%)

Accuracy

Total 0.0b remaining (68.8%)

Threshold costs 0.0b (68.8%)

Counts

38 → 1

Compiler

Compiled 8270 to 2696 computations (67.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end56.0ms (1.5%)

Compiler: Compiled 118 to 48 computations (59.3% saved)

Details

analyze2.0ms (0%)

sample635.0ms (16.6%)

simplify9.0ms (0.2%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series20.0ms (0.5%)

rewrite12.0ms (0.3%)

simplify95.0ms (2.5%)

prune223.0ms (5.8%)

localize7.0ms (0.2%)

series11.0ms (0.3%)

rewrite1.0ms (0%)

simplify102.0ms (2.7%)

prune29.0ms (0.7%)

localize14.0ms (0.4%)

series215.0ms (5.6%)

rewrite99.0ms (2.6%)

simplify265.0ms (6.9%)

prune396.0ms (10.3%)

localize12.0ms (0.3%)

series168.0ms (4.4%)

rewrite22.0ms (0.6%)

simplify156.0ms (4.1%)

prune1.1s (27.5%)

regimes217.0ms (5.7%)

simplify2.0ms (0.1%)

end56.0ms (1.5%)

Profiling