Details

analyze39.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
3	11	9

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`pow1/2_binary64`
5×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

1 → 36

Calls

1 calls:

23.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

series21.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

20.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

simplify175.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

700×	`sqr-pow_binary64`
489×	`associate-l_binary64`
475×	`distribute-rgt-out_binary64`
320×	`*-commutative_binary64`
313×	`cube-prod_binary64`

Counts

48 → 70

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	341
1	62	335
2	114	335
3	172	335
4	254	333
5	442	329
6	1113	329
7	1881	329
8	2104	329
9	2587	329
10	3186	329
11	3982	329
12	4779	329
13	4795	329

prune49.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	6	71

Error

0.2b

Counts

71 → 6

Alt Table

Status	Error	Program
	32.6b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
	33.6b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.6b	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))

Compiler

Compiled 580 to 436 computations (24.8% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) x)

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 35

Calls

1 calls:

27.0ms

(*.f64 (sqrt.f64 2) x)

series23.0ms (0.5%)

Counts

1 → 0

Calls

1 calls:

23.0ms

(*.f64 (sqrt.f64 2) x)

simplify107.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
478×	`prod-exp_binary64`
361×	`unswap-sqr_binary64`
355×	`exp-sum_binary64`
354×	`log-prod_binary64`

Counts

35 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	230
1	80	218
2	210	218
3	771	218
4	1708	218
5	3471	218
6	4793	218
7	4970	218

prune44.0ms (1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	44	10	54

Error

0.1b

Counts

54 → 10

Alt Table

Status	Error	Program
	30.6b	(neg.f64 (.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	33.6b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.6b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	30.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x))))
	30.6b	(neg.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3))
	30.6b	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))

Compiler

Compiled 551 to 449 computations (18.5% saved)

localize14.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

rewrite63.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`add-cbrt-cube_binary64`
8×	`prod-exp_binary64`

Counts

2 → 70

Calls

2 calls:

31.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
26.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)

series739.0ms (17.3%)

Counts

2 → 24

Calls

2 calls:

717.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
22.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

simplify145.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

893×	`exp-prod_binary64`
653×	`prod-exp_binary64`
482×	`fma-def_binary64`
475×	`distribute-lft-out_binary64`
346×	`*-commutative_binary64`

Counts

94 → 147

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	76	795
1	153	679
2	666	679
3	1298	679
4	2880	679
5	4383	663
6	5283	663

prune116.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	149	8	157

Error

0.1b

Counts

157 → 8

Alt Table

Status	Error	Program
	32.6b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
▶	30.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))))
	33.6b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	30.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x))))

Compiler

Compiled 1715 to 1559 computations (9.1% saved)

localize22.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))

rewrite108.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`prod-exp_binary64`
15×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`

Counts

3 → 105

Calls

3 calls:

37.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)))

31.0ms

(*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))

28.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)

series1.5s (35.7%)

Counts

3 → 36

Calls

3 calls:

820.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)

685.0ms

(*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))

23.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)))

simplify143.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

815×	`prod-exp_binary64`
577×	`*-commutative_binary64`
419×	`exp-prod_binary64`
398×	`log-prod_binary64`
249×	`associate-l_binary64`

Counts

141 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1821
1	244	1225
2	1220	1202
3	2912	1202
4	4973	1202

prune109.0ms (2.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	225	9	234

Error

0.1b

Counts

234 → 9

Alt Table

Status	Error	Program
	32.6b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
✓	30.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))))
	33.6b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	30.1b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	30.1b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.1b	(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3))))
	30.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x))))

Compiler

Compiled 3904 to 3691 computations (5.5% saved)

regimes126.0ms (2.9%)

Accuracy

Total 0.3b remaining (82.7%)

Threshold costs 0.3b (82.7%)

Compiler

Compiled 1127 to 950 computations (15.7% saved)

bsearch13.0ms (0.3%)

Steps

Iters	Range		Point
9	-8.914428672144927e-307	2.4518843920107785e-304	7.9778320587535e-311

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	35
1	30	35
2	44	35
3	53	35
4	59	35
5	61	35
6	61	35

end1.0ms (0%)

Compiler: Compiled 23 to 19 computations (17.4% saved)

sample578.0ms (13.5%)

Algorithm

1×

intervals

Results

243.0ms

8000×

body

128

valid

Compiler

Compiled 139 to 119 computations (14.4% saved)

Details

analyze39.0ms (0.9%)

sample23.0ms (0.5%)

simplify16.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite26.0ms (0.6%)

series21.0ms (0.5%)

simplify175.0ms (4.1%)

prune49.0ms (1.1%)

localize7.0ms (0.2%)

rewrite30.0ms (0.7%)

series23.0ms (0.5%)

simplify107.0ms (2.5%)

prune44.0ms (1%)

localize14.0ms (0.3%)

rewrite63.0ms (1.5%)

series739.0ms (17.3%)

simplify145.0ms (3.4%)

prune116.0ms (2.7%)

localize22.0ms (0.5%)

rewrite108.0ms (2.5%)

series1.5s (35.7%)

simplify143.0ms (3.3%)

prune109.0ms (2.5%)

regimes126.0ms (2.9%)

bsearch13.0ms (0.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample578.0ms (13.5%)

Profiling