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)

sample936.0ms (40.8%)

Results

891.0ms	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify18.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

417×	`times-frac_binary64`
412×	`associate-/l*_binary64`
360×	`associate-/r*_binary64`
350×	`associate-l_binary64`
200×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	19	9
2	50	9
3	111	7
4	236	7
5	531	7
6	1613	7

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.2%)

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))

series2.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

2.0ms

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

rewrite31.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

361×	`log1p-expm1-u_binary64`
361×	`expm1-log1p-u_binary64`
327×	`add-log-exp_binary64`
317×	`pow1_binary64`
205×	`unpow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	90	7
2	979	7

Stop Event

1×	node limit

Counts

1 → 49

Calls

1 calls:

30.0ms

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

simplify36.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

724×	`distribute-lft-out_binary64`
385×	`*-commutative_binary64`
380×	`fma-def_binary64`
341×	`distribute-rgt-out_binary64`
340×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	81
1	55	79
2	136	63
3	448	56
4	1828	56
5	3578	56
6	4583	56

Stop Event

1×	node limit

Counts

53 → 56

prune39.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Error

0.0b

Counts

57 → 3

Alt Table

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

Compiler

Compiled 767 to 564 computations (26.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series10.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

rewrite39.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`log1p-expm1-u_binary64`
528×	`expm1-log1p-u_binary64`
431×	`unpow-prod-down_binary64`
285×	`log-prod_binary64`
163×	`pow2_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	132	15
2	1482	13

Stop Event

1×	node limit

Counts

2 → 65

Calls

2 calls:

38.0ms	(pow.f64 (exp.f64 x) x)
38.0ms	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))

simplify37.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

512×	`fma-def_binary64`
439×	`*-commutative_binary64`
437×	`distribute-rgt-out_binary64`
424×	`associate-l_binary64`
349×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	244
1	84	216
2	208	200
3	592	195
4	2307	195
5	4558	195

Stop Event

1×	node limit

Counts

89 → 82

prune60.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	81	4	85

Error

0.0b

Counts

85 → 4

Alt Table

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

Compiler

Compiled 1226 to 775 computations (36.8% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 x 1/2)) (pow.f64 (.f64 (cbrt.f64 (exp.f64 x)) (exp.f64 x)) (.f64 x 1/2)))
✓	0.0b	(*.f64 (cbrt.f64 (exp.f64 x)) (exp.f64 x))
✓	0.0b	(pow.f64 (cbrt.f64 (exp.f64 x)) 2)
✓	0.1b	(cbrt.f64 (exp.f64 x))

series483.0ms (21.1%)

Counts

4 → 48

Calls

4 calls:

195.0ms	(*.f64 (cbrt.f64 (exp.f64 x)) (exp.f64 x))
146.0ms	(cbrt.f64 (exp.f64 x))
131.0ms	(pow.f64 (cbrt.f64 (exp.f64 x)) 2)
11.0ms	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 x 1/2)) (pow.f64 (.f64 (cbrt.f64 (exp.f64 x)) (exp.f64 x)) (.f64 x 1/2)))

rewrite57.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`log1p-expm1-u_binary64`
907×	`expm1-log1p-u_binary64`
116×	`add-sqr-sqrt_binary64`
112×	`add-cbrt-cube_binary64`
112×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	255	32
2	3172	32

Stop Event

1×	node limit

Counts

4 → 78

Calls

4 calls:

56.0ms	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 x 1/2)) (pow.f64 (.f64 (cbrt.f64 (exp.f64 x)) (exp.f64 x)) (.f64 x 1/2)))
56.0ms	(*.f64 (cbrt.f64 (exp.f64 x)) (exp.f64 x))
56.0ms	(pow.f64 (cbrt.f64 (exp.f64 x)) 2)
56.0ms	(cbrt.f64 (exp.f64 x))

simplify39.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

281×	`*-commutative_binary64`
269×	`fma-def_binary64`
209×	`associate-+l+_binary64`
205×	`distribute-rgt-out_binary64`
202×	`exp-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	644
1	187	554
2	480	423
3	1672	332
4	3985	332

Stop Event

1×	node limit

Counts

126 → 110

prune144.0ms (6.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	141	4	145

Error

0.0b

Counts

145 → 4

Alt Table

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

Compiler

Compiled 3432 to 2138 computations (37.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 (fma.f64 x x -1)))
	0.0b	(exp.f64 (fma.f64 x x -1))
✓	0.0b	(pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)

series10.0ms (0.4%)

Counts

2 → 16

Calls

2 calls:

6.0ms	(pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)
4.0ms	(sqrt.f64 (exp.f64 (fma.f64 x x -1)))

rewrite38.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

499×	`log1p-expm1-u_binary64`
499×	`expm1-log1p-u_binary64`
326×	`unpow-prod-down_binary64`
241×	`log-prod_binary64`
150×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	154	16
2	1418	16

Stop Event

1×	node limit

Counts

2 → 76

Calls

2 calls:

37.0ms	(sqrt.f64 (exp.f64 (fma.f64 x x -1)))
37.0ms	(pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)

simplify28.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
655×	`associate-l_binary64`
594×	`distribute-rgt-out_binary64`
468×	`associate-r_binary64`
285×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	247
1	98	243
2	260	213
3	876	192
4	3562	187

Stop Event

1×	node limit

Counts

92 → 90

prune125.0ms (5.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	146	4	150

Error

0.0b

Counts

150 → 4

Alt Table

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

Compiler

Compiled 2314 to 1815 computations (21.6% saved)

regimes57.0ms (2.5%)

Accuracy

Total 0.0b remaining (68.5%)

Threshold costs 0.0b (68.5%)

Counts

11 → 1

Compiler

Compiled 668 to 496 computations (25.7% 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

Stop Event

1×

saturated

end68.0ms (2.9%)

Compiler: Compiled 63 to 45 computations (28.6% saved)

Details

analyze5.0ms (0.2%)

sample936.0ms (40.8%)

simplify18.0ms (0.8%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite31.0ms (1.4%)

simplify36.0ms (1.6%)

prune39.0ms (1.7%)

localize6.0ms (0.2%)

series10.0ms (0.4%)

rewrite39.0ms (1.7%)

simplify37.0ms (1.6%)

prune60.0ms (2.6%)

localize13.0ms (0.6%)

series483.0ms (21.1%)

rewrite57.0ms (2.5%)

simplify39.0ms (1.7%)

prune144.0ms (6.3%)

localize6.0ms (0.2%)

series10.0ms (0.4%)

rewrite38.0ms (1.7%)

simplify28.0ms (1.2%)

prune125.0ms (5.4%)

regimes57.0ms (2.5%)

simplify2.0ms (0.1%)

end68.0ms (2.9%)

Profiling