Details

analyze26.0ms (1.3%)

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 10 to 5 computations (50% saved)

sample12.0ms (0.6%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 20 to 10 computations (50% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`count-2_binary64` `associate-r_binary64` `*-commutative_binary64`
1×	`distribute-rgt-out_binary64` `associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	9	9
2	12	9
3	13	9
4	13	9

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 21 to 12 computations (42.9% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

29.8b

(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite17.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

14.8b

Rules

4×	`pow1_binary64`
2×	`sqrt-pow1_binary64` `associate-*r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `sqrt-prod_binary64` `*-un-lft-identity_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 153 to 46 computations (69.9% saved)

series11.0ms (0.6%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

8.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 45 to 37 computations (17.8% saved)

simplify77.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

594×	`distribute-rgt-neg-in_binary64`
533×	`unsub-neg_binary64`
481×	`distribute-lft-neg-in_binary64`
404×	`neg-sub0_binary64`
402×	`neg-mul-1_binary64`

Counts

16 → 6

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	155
1	67	143
2	126	140
3	336	140
4	1155	140
5	2398	138
6	4346	138
7	5007	138

prune9.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	3	3	6
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	3	4	7

Error

16.2b

Counts

7 → 4

Alt Table

Status	Error	Program
	55.2b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))) x)
	42.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 3))
▶	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 92 to 66 computations (28.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.5b	(*.f64 x (sqrt.f64 2))

rewrite20.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
4×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`unswap-sqr_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

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

Compiler

Compiled 191 to 157 computations (17.8% saved)

series9.0ms (0.4%)

Error

16.2b

Counts

1 → 3

Calls

1 calls:

8.0ms

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

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify66.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

507×	`log-div_binary64`
340×	`log-prod_binary64`
331×	`associate-l_binary64`
288×	`unswap-sqr_binary64`
278×	`associate-*l/_binary64`

Counts

25 → 8

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	223
1	68	211
2	166	211
3	208	211
4	292	211
5	480	211
6	966	211
7	2596	211
8	3940	211
9	4921	211

prune11.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	6	2	8
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	6	6	12

Error

16.2b

Counts

12 → 6

Alt Table

Status	Error	Program
	63.2b	(neg.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 2) (sqrt.f64 x))))
▶	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	55.2b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))) x)
	42.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 3))
✓	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 149 to 107 computations (28.2% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite65.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1148 to 491 computations (57.2% saved)

series77.0ms (3.9%)

Error

16.2b

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt.f64 x)
18.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
16.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)

Compiler

Compiled 493 to 373 computations (24.3% saved)

simplify91.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

735×	`log-prod_binary64`
577×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
287×	`associate-l_binary64`

Counts

85 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	624
1	94	576
2	292	556
3	763	542
4	1759	418
5	4280	418
6	4543	418
7	4810	418

prune31.0ms (1.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	61	9	70

Error

16.1b

Counts

70 → 9

Alt Table

Status	Error	Program
✓	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	63.2b	(neg.f64 (.f64 (exp.f64 (.f64 2/3 (log.f64 x))) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	32.0b	(neg.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 5) (cbrt.f64 (cbrt.f64 x))) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	63.2b	(neg.f64 (.f64 (pow.f64 x 2/3) (.f64 (sqrt.f64 2) (cbrt.f64 x))))
	55.2b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))) x)
▶	32.0b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)) (.f64 (sqrt.f64 2) (cbrt.f64 x))))
	42.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 3))
✓	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
✓	30.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 626 to 397 computations (36.6% saved)

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)

rewrite57.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

16.1b

Rules

18×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow1/3_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`

Counts

4 → 57

Calls

4 calls:

4.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1350 to 622 computations (53.9% saved)

series90.0ms (4.6%)

Error

16.1b

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)
19.0ms	(cbrt.f64 x)
17.0ms	(cbrt.f64 x)
17.0ms	(cbrt.f64 x)

Compiler

Compiled 723 to 511 computations (29.3% saved)

simplify107.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

418×	`log-prod_binary64`
387×	`associate-+l+_binary64`
325×	`associate-+r+_binary64`
300×	`distribute-rgt-in_binary64`
274×	`distribute-lft-in_binary64`

Counts

69 → 47

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	65	610
1	118	585
2	252	571
3	673	569
4	1469	488
5	4543	488
6	4956	488
7	4934	488

prune24.0ms (1.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	46	10	56

Error

16.1b

Counts

56 → 10

Alt Table

Status	Error	Program
	31.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	63.2b	(neg.f64 (.f64 (exp.f64 (.f64 2/3 (log.f64 x))) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	32.0b	(neg.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 5) (cbrt.f64 (cbrt.f64 x))) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	63.2b	(neg.f64 (.f64 (pow.f64 x 2/3) (.f64 (sqrt.f64 2) (cbrt.f64 x))))
	55.2b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))) x)
	32.0b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)) (.f64 (sqrt.f64 2) (cbrt.f64 x))))
	42.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x x))) 3))
	63.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (exp.f64 (.f64 4 (log.f64 (cbrt.f64 (cbrt.f64 x)))))) (*.f64 (sqrt.f64 2) (cbrt.f64 x))))
	31.3b	(neg.f64 (*.f64 x (sqrt.f64 2)))
	30.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 600 to 344 computations (42.7% saved)

regimes559.0ms (28.3%)

Accuracy

Total -14.8b remaining (-4100.2%)

Threshold costs -14.8b (-4100.2%)

Compiler

Compiled 5730 to 3608 computations (37% saved)

bsearch13.0ms (0.7%)

Steps

Iters	Range		Point
9	-6.9717952857711765e-307	4.207346151756919e-305	1.25277216594145e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64` `sub-neg_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `+-commutative_binary64`
1×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	28	41
2	42	41
3	53	41
4	59	41
5	61	41
6	61	41

end1.0ms (0.1%)

Compiler: Compiled 26 to 21 computations (19.2% saved)

sample558.0ms (28.3%)

Algorithm

1×

intervals

Results

189.0ms

8000×

body

128

valid

Compiler

Compiled 165 to 117 computations (29.1% saved)

Details

analyze26.0ms (1.3%)

sample12.0ms (0.6%)

simplify8.0ms (0.4%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

rewrite17.0ms (0.8%)

series11.0ms (0.6%)

simplify77.0ms (3.9%)

prune9.0ms (0.4%)

localize4.0ms (0.2%)

rewrite20.0ms (1%)

series9.0ms (0.4%)

simplify66.0ms (3.4%)

prune11.0ms (0.5%)

localize8.0ms (0.4%)

rewrite65.0ms (3.3%)

series77.0ms (3.9%)

simplify91.0ms (4.6%)

prune31.0ms (1.6%)

localize14.0ms (0.7%)

rewrite57.0ms (2.9%)

series90.0ms (4.6%)

simplify107.0ms (5.4%)

prune24.0ms (1.2%)

regimes559.0ms (28.3%)

bsearch13.0ms (0.7%)

simplify5.0ms (0.3%)

end1.0ms (0.1%)

sample558.0ms (28.3%)

Profiling