Details

analyze6.0ms (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)

sample68.0ms (1.8%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify43.0ms (1.1%)

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))

series3.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

3.0ms

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

rewrite2.0ms (0%)

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))

simplify53.0ms (1.4%)

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

prune24.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	3	24

Error

0.0b

Counts

24 → 3

Alt Table

Status	Error	Program
	2.0b	(.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (cbrt.f64 (exp.f64 (fma.f64 x x -1)))) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
▶	0.0b	(pow.f64 (E.f64) (fma.f64 x x -1))
	63.3b	(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))

Compiler

Compiled 332 to 245 computations (26.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

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))

simplify72.0ms (1.9%)

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

prune179.0ms (4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Error

0.0b

Counts

40 → 3

Alt Table

Status	Error	Program
▶	2.0b	(.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (cbrt.f64 (exp.f64 (fma.f64 x x -1)))) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
✓	0.0b	(pow.f64 (E.f64) (fma.f64 x x -1))
	63.3b	(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))

Compiler

Compiled 496 to 334 computations (32.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (cbrt.f64 (exp.f64 (fma.f64 x x -1)))) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
✓	0.0b	(*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
	0.0b	(exp.f64 (fma.f64 x x -1))
✓	1.0b	(cbrt.f64 (exp.f64 (fma.f64 x x -1)))

series636.0ms (17%)

Counts

3 → 36

Calls

3 calls:

352.0ms

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

280.0ms

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

3.0ms

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

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`cbrt-prod_binary64`
29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
16×	`pow1/3_binary64`
14×	`associate-r_binary64`

Counts

3 → 98

Calls

3 calls:

8.0ms

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

8.0ms

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

1.0ms

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

simplify153.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
551×	`unswap-sqr_binary64`
502×	`log-prod_binary64`
389×	`exp-sum_binary64`
359×	`exp-prod_binary64`

Counts

134 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	132	2132
1	268	2050
2	723	1818
3	1486	1652
4	3597	1361
5	4234	1361
6	4865	1361
7	4991	1361
8	4839	1361

prune219.0ms (5.9%)

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
✓	0.0b	(pow.f64 (E.f64) (fma.f64 x x -1))
	63.3b	(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
▶	2.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1)))) 4) (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3))) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))

Compiler

Compiled 6724 to 4951 computations (26.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1)))) 4)
✓	0.0b	(pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)
✓	1.0b	(cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
	1.0b	(cbrt.f64 (exp.f64 (fma.f64 x x -1)))

series757.0ms (20.2%)

Counts

3 → 36

Calls

3 calls:

276.0ms	(pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)
240.0ms	(cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
239.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1)))) 4)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cbrt-prod_binary64`
14×	`unpow-prod-down_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 67

Calls

3 calls:

3.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1)))) 4)
2.0ms	(pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)
2.0ms	(cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))))

simplify142.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

542×	`log-prod_binary64`
372×	`associate-l_binary64`
346×	`associate-r_binary64`
329×	`exp-prod_binary64`
319×	`fma-def_binary64`

Counts

103 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1652
1	314	1585
2	727	1536
3	2335	1460
4	4099	1460
5	4896	1460
6	4965	1460
7	5161	1460

prune158.0ms (4.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	174	3	177

Error

0.0b

Counts

177 → 3

Alt Table

Status	Error	Program
✓	0.0b	(pow.f64 (E.f64) (fma.f64 x x -1))
	63.3b	(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
✓	2.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1)))) 4) (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3))) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))

Compiler

Compiled 5573 to 4341 computations (22.1% saved)

regimes524.0ms (14%)

Accuracy

Total -0.0b remaining (-4.7%)

Threshold costs -0.0b (-4.7%)

Counts

113 → 1

Compiler

Compiled 11326 to 8464 computations (25.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13
2	13	13
3	12	13

end0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample623.0ms (16.7%)

Algorithm

1×

intervals

Results

367.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 65 to 49 computations (24.6% saved)

Details

analyze6.0ms (0.2%)

sample68.0ms (1.8%)

simplify43.0ms (1.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite2.0ms (0%)

simplify53.0ms (1.4%)

prune24.0ms (0.6%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite2.0ms (0.1%)

simplify72.0ms (1.9%)

prune179.0ms (4.8%)

localize8.0ms (0.2%)

series636.0ms (17%)

rewrite28.0ms (0.8%)

simplify153.0ms (4.1%)

prune219.0ms (5.9%)

localize14.0ms (0.4%)

series757.0ms (20.2%)

rewrite9.0ms (0.3%)

simplify142.0ms (3.8%)

prune158.0ms (4.2%)

regimes524.0ms (14%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample623.0ms (16.7%)

Profiling