Details

analyze5.0ms (0.3%)

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)

sample1.1s (55.5%)

Results

1.0s	8256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify42.0ms (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))

series3.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

3.0ms

(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))

simplify55.0ms (2.9%)

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

prune18.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	0	0
Picked	0	1	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	(exp.f64 (fma.f64 x x -1))
▶	0.0b	(.f64 (exp.f64 (.f64 x x)) (exp.f64 -1))

Compiler

Compiled 314 to 233 computations (25.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(.f64 (exp.f64 (.f64 x x)) (exp.f64 -1))
4.0ms	(exp.f64 (*.f64 x x))

rewrite7.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`pow1_binary64`

Counts

2 → 32

Calls

2 calls:

5.0ms	(.f64 (exp.f64 (.f64 x x)) (exp.f64 -1))
1.0ms	(exp.f64 (*.f64 x x))

simplify66.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

839×	`fma-def_binary64`
478×	`distribute-rgt-in_binary64`
436×	`unswap-sqr_binary64`
393×	`distribute-lft-in_binary64`
249×	`exp-sum_binary64`

Counts

56 → 58

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	67	564
1	152	511
2	383	495
3	1042	490
4	2439	490
5	4633	489
6	4916	489

prune33.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	59	2	61

Error

0.0b

Counts

61 → 2

Alt Table

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

Compiler

Compiled 711 to 430 computations (39.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
2.0ms	(pow.f64 (exp.f64 x) x)

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-l_binary64`
7×	`unpow-prod-down_binary64`

Counts

2 → 49

Calls

2 calls:

7.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
2.0ms	(pow.f64 (exp.f64 x) x)

simplify68.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

458×	`distribute-rgt-in_binary64`
413×	`distribute-lft-in_binary64`
393×	`associate-l_binary64`
328×	`associate-r_binary64`
324×	`prod-exp_binary64`

Counts

73 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	94	814
1	207	728
2	546	712
3	1685	705
4	4496	700
5	5060	700

prune57.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	90	3	93

Error

Counts

93 → 3

Alt Table

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

Compiler

Compiled 1160 to 659 computations (43.2% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series23.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

8.0ms	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (exp.f64 -1))
7.0ms	(sqrt.f64 (pow.f64 (exp.f64 x) x))
7.0ms	(.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (exp.f64 -1)))

rewrite25.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`associate-l_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

10.0ms	(.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (exp.f64 -1)))
8.0ms	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (exp.f64 -1))
2.0ms	(sqrt.f64 (pow.f64 (exp.f64 x) x))

simplify114.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

678×	`distribute-rgt-in_binary64`
596×	`fma-def_binary64`
572×	`unswap-sqr_binary64`
255×	`*-commutative_binary64`
158×	`sqr-pow_binary64`

Counts

114 → 141

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	1741
1	291	1536
2	736	1440
3	1237	1417
4	2375	1388
5	4794	1388
6	4996	1388
7	4903	1388

prune168.0ms (8.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	259	3	262

Error

Counts

262 → 3

Alt Table

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

Compiler

Compiled 5008 to 2072 computations (58.6% saved)

regimes67.0ms (3.5%)

Accuracy

Total 0.0b remaining (63%)

Threshold costs 0.0b (63%)

Counts

12 → 1

Compiler

Compiled 776 to 557 computations (28.2% saved)

simplify2.0ms (0.1%)

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

end49.0ms (2.5%)

Compiler: Compiled 45 to 30 computations (33.3% saved)

Details

analyze5.0ms (0.3%)

sample1.1s (55.5%)

simplify42.0ms (2.2%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite2.0ms (0.1%)

simplify55.0ms (2.9%)

prune18.0ms (0.9%)

localize5.0ms (0.3%)

series9.0ms (0.5%)

rewrite7.0ms (0.4%)

simplify66.0ms (3.4%)

prune33.0ms (1.7%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite11.0ms (0.6%)

simplify68.0ms (3.5%)

prune57.0ms (3%)

localize8.0ms (0.4%)

series23.0ms (1.2%)

rewrite25.0ms (1.3%)

simplify114.0ms (5.9%)

prune168.0ms (8.7%)

regimes67.0ms (3.5%)

simplify2.0ms (0.1%)

end49.0ms (2.5%)

Profiling