Details

analyze4.0ms (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
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)

sample704.0ms (33.3%)

Results

667.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify7.0ms (0.3%)

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

prune2.0ms (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

31.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.2b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	30.1b	(sqrt.f64 (.f64 (.f64 2 x) x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64`
3×	`sqrt-pow1_binary64`
3×	`pow-prod-down_binary64`
1×	`*-un-lft-identity_binary64`
1×	`sqrt-prod_binary64`

Counts

1 → 14

Calls

1 calls:

3.0ms

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

simplify161.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
575×	`cube-prod_binary64`
527×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

26 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	211
1	36	205
2	63	205
3	79	205
4	87	205
5	114	205
6	145	205
7	203	205
8	414	205
9	768	205
10	776	205
11	906	205
12	1060	205
13	1223	205
14	1451	205
15	1752	205
16	2100	205
17	2575	205
18	3193	205
19	3389	205
20	3563	205
21	3677	205
22	3724	205
23	3776	205
24	4654	205
25	4739	205
26	4663	205

prune27.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	17	5	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	6	23

Error

0.2b

Counts

23 → 6

Alt Table

Status	Error	Program
	33.5b	(*.f64 (sqrt.f64 2) x)
✓	31.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	31.8b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
▶	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 350 to 263 computations (24.9% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

6.0ms

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

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 24

Calls

1 calls:

7.0ms

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

simplify57.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

444×	`cube-div_binary64`
431×	`log-div_binary64`
332×	`associate-l_binary64`
303×	`log-prod_binary64`
288×	`unswap-sqr_binary64`

Counts

24 → 25

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	226
1	67	214
2	159	214
3	214	214
4	293	214
5	479	214
6	964	214
7	2475	214
8	3811	214
9	4892	214

prune19.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	23	8	31

Error

0.1b

Counts

31 → 8

Alt Table

Status	Error	Program
	29.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	33.5b	(*.f64 (sqrt.f64 2) x)
	30.1b	(neg.f64 (.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
✓	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	31.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
▶	29.6b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))

Compiler

Compiled 404 to 332 computations (17.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series8.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

rewrite15.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
15×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)

simplify77.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

455×	`log-div_binary64`
454×	`cube-div_binary64`
378×	`log-prod_binary64`
365×	`associate-l_binary64`
364×	`cube-prod_binary64`

Counts

66 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	697
1	126	642
2	352	642
3	548	642
4	651	642
5	907	642
6	2188	642
7	3602	642
8	4934	642

prune42.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	76	7	83

Error

0.1b

Counts

83 → 7

Alt Table

Status	Error	Program
▶	29.6b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (sqrt.f64 2)) x))))
✓	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.5b	(*.f64 (sqrt.f64 2) x)
✓	31.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	29.6b	(neg.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) x))

Compiler

Compiled 1267 to 1137 computations (10.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series520.0ms (24.6%)

Counts

2 → 24

Calls

2 calls:

517.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (sqrt.f64 2)) x)))

rewrite28.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`sqrt-prod_binary64`
24×	`associate-l_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`

Counts

2 → 61

Calls

2 calls:

15.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (sqrt.f64 2)) x)))
9.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

simplify111.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

761×	`unswap-sqr_binary64`
469×	`associate-/l*_binary64`
339×	`*-commutative_binary64`
274×	`associate-/l/_binary64`
252×	`sqr-pow_binary64`

Counts

85 → 87

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	79	1437
1	188	1044
2	539	1044
3	790	1044
4	1076	1044
5	1749	1044
6	4023	1038
7	4290	970
8	5000	970
9	5100	970

prune82.0ms (3.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	125	7	132

Error

0.1b

Counts

132 → 7

Alt Table

Status	Error	Program
✓	29.6b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (sqrt.f64 2)) x))))
✓	29.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.5b	(*.f64 (sqrt.f64 2) x)
✓	31.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	29.6b	(neg.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) x))

Compiler

Compiled 2760 to 2571 computations (6.8% saved)

regimes91.0ms (4.3%)

Accuracy

Total 0.3b remaining (83.3%)

Threshold costs 0.3b (83.3%)

Counts

18 → 2

Compiler

Compiled 840 to 686 computations (18.3% saved)

bsearch15.0ms (0.7%)

Steps

Iters	Range		Point
9	-2.0528680884149487e-305	3.619234184467057e-306	-3.93452588565997e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.2%)

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	20	43
1	32	43
2	46	43
3	55	43
4	61	43
5	63	43
6	63	43

end95.0ms (4.5%)

Compiler: Compiled 124 to 104 computations (16.1% saved)

Details

analyze4.0ms (0.2%)

sample704.0ms (33.3%)

simplify7.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify161.0ms (7.6%)

prune27.0ms (1.3%)

localize7.0ms (0.3%)

series6.0ms (0.3%)

rewrite8.0ms (0.4%)

simplify57.0ms (2.7%)

prune19.0ms (0.9%)

localize5.0ms (0.3%)

series8.0ms (0.4%)

rewrite15.0ms (0.7%)

simplify77.0ms (3.6%)

prune42.0ms (2%)

localize7.0ms (0.3%)

series520.0ms (24.6%)

rewrite28.0ms (1.3%)

simplify111.0ms (5.2%)

prune82.0ms (3.9%)

regimes91.0ms (4.3%)

bsearch15.0ms (0.7%)

simplify5.0ms (0.2%)

end95.0ms (4.5%)

Profiling