Details

analyze56.0ms (2.7%)

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)

sample17.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify45.0ms (2.2%)

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 (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(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))

series3.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

3.0ms

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

simplify83.0ms (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 → 24

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

prune21.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	21	3	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	3	25

Error

0.0b

Counts

25 → 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	(cbrt.f64 (.f64 (.f64 (exp.f64 (fma.f64 x x -1)) (exp.f64 (fma.f64 x x -1))) (exp.f64 (fma.f64 x x -1))))
	0.0b	(pow.f64 E.f64 (fma.f64 x x -1))

Compiler

Compiled 344 to 253 computations (26.5% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 (fma.f64 x x -1))
✓	0.0b	(*.f64 (exp.f64 (fma.f64 x x -1)) (exp.f64 (fma.f64 x x -1)))
✓	1.0b	(.f64 (.f64 (exp.f64 (fma.f64 x x -1)) (exp.f64 (fma.f64 x x -1))) (exp.f64 (fma.f64 x x -1)))
✓	1.6b	(cbrt.f64 (.f64 (.f64 (exp.f64 (fma.f64 x x -1)) (exp.f64 (fma.f64 x x -1))) (exp.f64 (fma.f64 x x -1))))

rewrite33.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`exp-prod_binary64`
29×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 92

Calls

3 calls:

10.0ms

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

10.0ms

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

8.0ms

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

series27.0ms (1.3%)

Counts

3 → 36

Calls

3 calls:

16.0ms

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

9.0ms

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

2.0ms

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

simplify113.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

459×	`exp-sum_binary64`
373×	`associate-+l+_binary64`
365×	`fma-def_binary64`
337×	`log-prod_binary64`
318×	`*-commutative_binary64`

Counts

128 → 215

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	132	1684
1	298	1399
2	823	1341
3	1786	1285
4	3137	1207
5	4719	1207
6	4860	1207

prune146.0ms (7.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	239	3	242

Error

Counts

242 → 3

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (.f64 (.f64 (exp.f64 (fma.f64 x x -1)) (exp.f64 (fma.f64 x x -1))) (exp.f64 (fma.f64 x x -1))))
	0.0b	(pow.f64 E.f64 (fma.f64 x x -1))
▶	0.0b	(cbrt.f64 (pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3)))

Compiler

Compiled 3545 to 2556 computations (27.9% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 x x -1) 3)
✓	1.0b	(pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3))
✓	1.6b	(cbrt.f64 (pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3)))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

3 → 57

Calls

3 calls:

3.0ms	(*.f64 (fma.f64 x x -1) 3)
2.0ms	(pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3))
2.0ms	(cbrt.f64 (pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3)))

series381.0ms (18.5%)

Counts

3 → 36

Calls

3 calls:

366.0ms	(cbrt.f64 (pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3)))
11.0ms	(*.f64 (fma.f64 x x -1) 3)
4.0ms	(pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3))

simplify90.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

391×	`associate-l_binary64`
339×	`associate-r_binary64`
263×	`associate-+l+_binary64`
244×	`fma-def_binary64`
242×	`associate-+r+_binary64`

Counts

93 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1379
1	227	1132
2	633	1089
3	2353	1062
4	4366	1062
5	4878	1062

prune81.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	165	3	168

Error

Counts

168 → 3

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (.f64 (.f64 (exp.f64 (fma.f64 x x -1)) (exp.f64 (fma.f64 x x -1))) (exp.f64 (fma.f64 x x -1))))
▶	0.0b	(pow.f64 E.f64 (fma.f64 x x -1))
✓	0.0b	(cbrt.f64 (pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3)))

Compiler

Compiled 1722 to 1383 computations (19.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(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))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

simplify79.0ms (3.9%)

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 → 51

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

prune29.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	51	3	54

Error

Counts

54 → 3

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (.f64 (.f64 (exp.f64 (fma.f64 x x -1)) (exp.f64 (fma.f64 x x -1))) (exp.f64 (fma.f64 x x -1))))
✓	0.0b	(pow.f64 E.f64 (fma.f64 x x -1))
✓	0.0b	(cbrt.f64 (pow.f64 (exp.f64 1) (*.f64 (fma.f64 x x -1) 3)))

Compiler

Compiled 458 to 308 computations (32.8% saved)

regimes270.0ms (13.1%)

Accuracy

Total 0.0b remaining (36%)

Threshold costs 0.0b (36%)

Compiler

Compiled 4905 to 3769 computations (23.2% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample539.0ms (26.2%)

Algorithm

1×

intervals

Results

314.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 55 to 41 computations (25.5% saved)

Details

analyze56.0ms (2.7%)

sample17.0ms (0.8%)

simplify45.0ms (2.2%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

rewrite2.0ms (0.1%)

series3.0ms (0.1%)

simplify83.0ms (4%)

prune21.0ms (1%)

localize8.0ms (0.4%)

rewrite33.0ms (1.6%)

series27.0ms (1.3%)

simplify113.0ms (5.5%)

prune146.0ms (7.1%)

localize8.0ms (0.4%)

rewrite10.0ms (0.5%)

series381.0ms (18.5%)

simplify90.0ms (4.4%)

prune81.0ms (3.9%)

localize4.0ms (0.2%)

rewrite2.0ms (0.1%)

series4.0ms (0.2%)

simplify79.0ms (3.9%)

prune29.0ms (1.4%)

regimes270.0ms (13.1%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample539.0ms (26.2%)

Profiling