Details

analyze5.0ms (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
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50%	0.4%	49.6%	10
50.2%	0.2%	49.6%	11
50.2%	0.1%	49.7%	12
50.2%	0%	49.8%	13
50.2%	0%	49.8%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample103.0ms (3.9%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify46.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

668×	`div-sub_binary64`
499×	`fma-def_binary64`
417×	`times-frac_binary64`
411×	`associate-/l*_binary64`
366×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	19	9
2	45	9
3	89	7
4	191	7
5	438	7
6	1294	7
7	3635	7
8	5317	7

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 25 to 17 computations (32% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 x x -1))

series2.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

2.0ms

(exp.f64 (fma.f64 x x -1))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`exp-prod_binary64`
2×	`add-log-exp_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 14

Calls

1 calls:

1.0ms

(exp.f64 (fma.f64 x x -1))

simplify59.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

431×	`fma-def_binary64`
418×	`exp-sum_binary64`
378×	`associate-l_binary64`
330×	`unswap-sqr_binary64`
324×	`distribute-lft-out_binary64`

Counts

18 → 23

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	221
1	84	206
2	178	190
3	528	183
4	1777	183
5	4482	183
6	5315	183

prune19.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	4	24

Error

0.0b

Counts

24 → 4

Alt Table

Status	Error	Program
	1.2b	(exp.f64 -1)
	63.3b	(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
✓	0.0b	(exp.f64 (fma.f64 x x -1))
▶	0.1b	(pow.f64 (E.f64) (fma.f64 x x -1))

Compiler

Compiled 302 to 225 computations (25.5% saved)

localize10.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (E.f64) (fma.f64 x x -1))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(pow.f64 (E.f64) (fma.f64 x x -1))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`pow-unpow_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`unpow-prod-down_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 21

Calls

1 calls:

2.0ms

(pow.f64 (E.f64) (fma.f64 x x -1))

simplify73.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-def_binary64`
320×	`associate-/l/_binary64`
256×	`*-commutative_binary64`
223×	`distribute-rgt-in_binary64`
209×	`fma-neg_binary64`

Counts

33 → 37

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	399
1	124	364
2	296	347
3	969	338
4	2686	337
5	4811	337
6	4986	337
7	4872	337

prune30.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	38	3	41

Error

0.0b

Counts

41 → 3

Alt Table

Status	Error	Program
	0.1b	(*.f64 (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))))
▶	0.0b	(*.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)))
✓	0.0b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 491 to 327 computations (33.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)))
✓	0.0b	(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1))

series20.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

13.0ms	(*.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)))
6.0ms	(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`unpow-prod-down_binary64`
45×	`add-sqr-sqrt_binary64`
25×	`sqrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 101

Calls

2 calls:

9.0ms	(*.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)))
2.0ms	(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1))

simplify139.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l/_binary64`
322×	`times-frac_binary64`
303×	`*-commutative_binary64`
293×	`distribute-rgt-in_binary64`
270×	`distribute-lft-in_binary64`

Counts

125 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	2894
1	299	2706
2	1057	2652
3	2757	2618
4	4913	2618
5	4980	2618
6	4912	2618

prune145.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	162	3	165

Error

0.0b

Counts

165 → 3

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))))
✓	0.0b	(exp.f64 (fma.f64 x x -1))
	2.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) 2)) (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) 2))) (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) 2)))

Compiler

Compiled 3955 to 2166 computations (45.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1)))
✓	0.0b	(*.f64 (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))))
	0.1b	(pow.f64 (E.f64) (fma.f64 x x -1))

series9.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1)))
4.0ms	(*.f64 (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-prod_binary64`
62×	`add-sqr-sqrt_binary64`
32×	`unpow-prod-down_binary64`
27×	`rem-sqrt-square_binary64`
22×	`sqr-pow_binary64`

Counts

2 → 110

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))))
2.0ms	(sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1)))

simplify137.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

948×	`fma-def_binary64`
486×	`unswap-sqr_binary64`
438×	`associate-l_binary64`
435×	`*-commutative_binary64`
345×	`associate-r_binary64`

Counts

134 → 152

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	137	2235
1	241	2136
2	717	2045
3	1601	1944
4	3391	1840
5	4626	1812
6	4956	1812
7	4902	1812

prune323.0ms (12.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	265	1	266
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	266	3	269

Error

0.0b

Counts

269 → 3

Alt Table

Status	Error	Program
	0.3b	(cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1)))) (.f64 (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))))) (*.f64 (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 x x -1))))))
✓	0.0b	(exp.f64 (fma.f64 x x -1))
	2.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) 2)) (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) 2))) (cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 x x -1)) 2)))

Compiler

Compiled 5557 to 3622 computations (34.8% saved)

regimes862.0ms (32.7%)

Accuracy

Total 0.0b remaining (53.5%)

Threshold costs 0.0b (53.5%)

Counts

198 → 1

Compiler

Compiled 20261 to 14670 computations (27.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	15	18
2	17	18
3	16	18

end1.0ms (0%)

Compiler: Compiled 12 to 10 computations (16.7% saved)

sample580.0ms (22%)

Algorithm

1×

intervals

Results

313.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 110 to 77 computations (30% saved)

Details

analyze5.0ms (0.2%)

sample103.0ms (3.9%)

simplify46.0ms (1.7%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series2.0ms (0.1%)

rewrite2.0ms (0.1%)

simplify59.0ms (2.2%)

prune19.0ms (0.7%)

localize10.0ms (0.4%)

series4.0ms (0.2%)

rewrite2.0ms (0.1%)

simplify73.0ms (2.8%)

prune30.0ms (1.1%)

localize7.0ms (0.3%)

series20.0ms (0.7%)

rewrite21.0ms (0.8%)

simplify139.0ms (5.3%)

prune145.0ms (5.5%)

localize6.0ms (0.2%)

series9.0ms (0.4%)

rewrite22.0ms (0.8%)

simplify137.0ms (5.2%)

prune323.0ms (12.2%)

regimes862.0ms (32.7%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample580.0ms (22%)

Profiling