Details

analyze114.0ms (2.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample51.0ms (1.1%)

Algorithm

1×

intervals

Results

16.0ms	49×	body	2048	valid
10.0ms	53×	body	1024	valid
4.0ms	36×	body	512	valid
3.0ms	24×	body	256	valid
3.0ms	94×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
455×	`*-commutative_binary64`
440×	`unswap-sqr_binary64`
344×	`associate-l_binary64`
274×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	16	6
2	23	6
3	35	6
4	70	6
5	160	6
6	432	6
7	1564	6
8	3490	6
9	4954	6
10	4993	6
11	4874	6

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (*.f64 a x))
	30.2b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 40 to 27 computations (32.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64`
5×	`expm1-udef_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`log1p-expm1-u_binary64`

Counts

1 → 32

Calls

1 calls:

9.0ms

(expm1.f64 (*.f64 a x))

series8.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(expm1.f64 (*.f64 a x))

simplify109.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-neg_binary64`
419×	`*-commutative_binary64`
328×	`unswap-sqr_binary64`
262×	`cancel-sign-sub-inv_binary64`
223×	`sqr-pow_binary64`

Counts

56 → 85

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	57	533
1	133	511
2	353	502
3	1186	498
4	2098	484
5	3131	484
6	4771	472
7	4996	472
8	4931	472

prune21.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Error

0.0b

Counts

87 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
	44.0b	(pow.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)
▶	20.8b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))

Compiler

Compiled 490 to 208 computations (57.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
✓	0.2b	(pow.f64 (*.f64 a x) 2)

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`

Counts

2 → 74

Calls

2 calls:

14.0ms	(pow.f64 (*.f64 a x) 2)
9.0ms	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))

series99.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

75.0ms	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
24.0ms	(pow.f64 (*.f64 a x) 2)

simplify114.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

465×	`unswap-sqr_binary64`
347×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
288×	`distribute-rgt-neg-in_binary64`
281×	`distribute-lft-neg-in_binary64`

Counts

122 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	1181
1	159	1136
2	592	1126
3	1711	1126
4	4594	1126
5	4989	1126
6	4957	1126

prune45.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	201	3	204

Error

0.0b

Counts

204 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	44.0b	(pow.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)
✓	20.8b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))

Compiler

Compiled 1433 to 803 computations (44% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x)))
✓	0.2b	(.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (*.f64 a x)))
✓	25.0b	(pow.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary64`
19×	`add-exp-log_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 121

Calls

3 calls:

14.0ms

(pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)

12.0ms

(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))

12.0ms

(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))

series776.0ms (16.5%)

Counts

3 → 72

Calls

3 calls:

721.0ms

(pow.f64 (*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x))) 1/3)

38.0ms

(*.f64 (*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x))) (expm1.f64 (*.f64 a x)))

17.0ms

(*.f64 (expm1.f64 (*.f64 a x)) (expm1.f64 (*.f64 a x)))

simplify129.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-def_binary64`
471×	`unswap-sqr_binary64`
466×	`exp-prod_binary64`
365×	`*-commutative_binary64`
338×	`log-prod_binary64`

Counts

193 → 339

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	174	2399
1	354	2178
2	1035	1867
3	3135	1770
4	4386	1760
5	5063	1760

prune108.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	422	2	424
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	423	4	427

Error

0.0b

Counts

427 → 4

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	20.8b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
▶	38.8b	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	50.8b	(pow.f64 (pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3) 1/3)

Compiler

Compiled 4176 to 1526 computations (63.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	10.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 2/3)
✓	10.3b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

rewrite73.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
10×	`pow1/3_binary64`
9×	`add-exp-log_binary64`
9×	`log1p-expm1-u_binary64`

Counts

3 → 104

Calls

3 calls:

42.0ms	(cbrt.f64 (expm1.f64 (*.f64 a x)))
13.0ms	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
11.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 2/3)

series1.3s (27.7%)

Counts

3 → 72

Calls

3 calls:

671.0ms	(cbrt.f64 (expm1.f64 (*.f64 a x)))
631.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 2/3)
6.0ms	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))

simplify118.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
524×	`distribute-rgt-in_binary64`
521×	`unswap-sqr_binary64`
491×	`distribute-lft-in_binary64`
378×	`*-commutative_binary64`

Counts

176 → 295

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2248
1	367	2140
2	1031	1810
3	2533	1697
4	4928	1697
5	5020	1697

prune94.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	464	1	465
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	465	4	469

Error

0.0b

Counts

469 → 4

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
	38.8b	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (pow.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x)))) 2))
✓	20.8b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
	50.8b	(pow.f64 (pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3) 1/3)

Compiler

Compiled 3328 to 1300 computations (60.9% saved)

regimes57.0ms (1.2%)

Accuracy

Total 0.0b remaining (45.3%)

Threshold costs 0.0b (45.3%)

Compiler

Compiled 708 to 471 computations (33.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

end6.0ms (0.1%)

Remove: (sort a x)
Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.3s (27.5%)

Algorithm

1×

intervals

Results

459.0ms	1455×	body	2048	valid
292.0ms	1727×	body	1024	valid
109.0ms	1093×	body	512	valid
97.0ms	3070×	body	128	valid
42.0ms	655×	body	256	valid
5.0ms	128×	body	128	invalid

Compiler

Compiled 64 to 46 computations (28.1% saved)

Details

analyze114.0ms (2.4%)

sample51.0ms (1.1%)

simplify79.0ms (1.7%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

rewrite10.0ms (0.2%)

series8.0ms (0.2%)

simplify109.0ms (2.3%)

prune21.0ms (0.5%)

localize6.0ms (0.1%)

rewrite26.0ms (0.5%)

series99.0ms (2.1%)

simplify114.0ms (2.4%)

prune45.0ms (0.9%)

localize7.0ms (0.2%)

rewrite45.0ms (1%)

series776.0ms (16.5%)

simplify129.0ms (2.7%)

prune108.0ms (2.3%)

localize7.0ms (0.2%)

rewrite73.0ms (1.5%)

series1.3s (27.7%)

simplify118.0ms (2.5%)

prune94.0ms (2%)

regimes57.0ms (1.2%)

simplify3.0ms (0.1%)

end6.0ms (0.1%)

sample1.3s (27.5%)

Profiling