Details

analyze4.0ms

Algorithm

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

sample10.0ms

Algorithm

intervals

Results

5.0ms

256×

body

128

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

prune2.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.4b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

26.6b

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1_binary64`
3×	`pow-prod-down_binary64` `sqrt-pow1_binary64`
1×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

4.0ms

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

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify147.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4798	123
1	4798	123

prune20.0ms

Filtered

11 candidates to 15 candidates (-36.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	10	5	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	6	16

Merged error: 0.2b

Counts

16 → 6

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))
26.6b	(sqrt.f64 (.f64 x (.f64 2 x)))
26.6b	(sqrt.f64 (.f64 x (.f64 2 x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

158×	`pow1_binary64`
154×	`sqrt-pow1_binary64`
82×	`pow-prod-down_binary64`
33×	`sqrt-prod_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`pow1/2_binary64`
21×	`pow-prod-up_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `pow-sqr_binary64`
9×	`swap-sqr_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 130

Calls

4 calls:

5.0ms	(sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))
17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))
4.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
4.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))
54.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))
41.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
48.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4963	1273
1	4963	1273

prune73.0ms

Filtered

67 candidates to 142 candidates (-111.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	140	8	148

Merged error: 0.2b

Counts

148 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2))))) 3))
0.8b	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))) 3)
26.6b	(sqrt.f64 (.f64 x (.f64 2 x)))
26.6b	(sqrt.f64 (.f64 x (.f64 x 2)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

104×	`sqrt-prod_binary64`
66×	`add-sqr-sqrt_binary64`
29×	`unpow-prod-down_binary64` `cube-prod_binary64`
26×	`associate-r_binary64`
25×	`pow1_binary64`
24×	`unswap-sqr_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64`
10×	`add-exp-log_binary64` `associate-l_binary64`
9×	`pow-prod-down_binary64` `pow-pow_binary64`
7×	`add-cbrt-cube_binary64`
5×	`pow1/2_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `prod-exp_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-unprod_binary64` `sqrt-pow2_binary64` `rem-cube-cbrt_binary64` `*-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2))))) 3))
9.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))) 3)
4.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
4.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2))))) 3))
325.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))) 3)
48.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
43.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))

simplify88.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4906	2549
1	4906	2549

prune99.0ms

Filtered

70 candidates to 154 candidates (-120.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	154	8	162

Merged error: 0.2b

Counts

162 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2))))) 3/2))
26.6b	(sqrt.f64 (.f64 x (.f64 2 x)))
26.6b	(sqrt.f64 (.f64 x (.f64 x 2)))
26.6b	(sqrt.f64 (.f64 x (.f64 x 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod_binary64`
82×	`unpow-prod-down_binary64`
72×	`add-sqr-sqrt_binary64`
25×	`unswap-sqr_binary64`
22×	`pow1_binary64`
20×	`*-un-lft-identity_binary64` `swap-sqr_binary64` `add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
14×	`associate-r_binary64` `sqr-pow_binary64` `associate-l_binary64`
10×	`pow-prod-down_binary64`
9×	`sqrt-pow1_binary64` `prod-exp_binary64`
6×	`pow-to-exp_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64`
3×	`pow1/2_binary64`
1×	`cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 131

Calls

4 calls:

17.0ms	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2))))) 3/2))
4.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
4.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))
4.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (.f64 x 2))))) 3/2) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 x 2))))) 3/2))
41.0ms	(sqrt.f64 (.f64 x (.f64 2 x)))
42.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))
47.0ms	(sqrt.f64 (.f64 x (.f64 x 2)))

simplify90.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4890	3466
1	4890	3466

prune136.0ms

Filtered

73 candidates to 143 candidates (-95.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	143	8	151

Merged error: 0.2b

Counts

151 → 8

regimes80.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 30.6b

bsearch14.0ms

Steps

Iters	Range		Point
10	-5.6214953350431465e-304	1.0086025560860257e-295	-2.72459992856335e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	25
1	40	25

end0.0ms

sample265.0ms

Algorithm

intervals

Results

177.0ms

8000×

body

128

valid

Details

analyze4.0ms

sample10.0ms

simplify8.0ms

prune2.0ms

localize4.0ms

rewrite5.0ms

series47.0ms

simplify147.0ms

prune20.0ms

localize7.0ms

rewrite43.0ms

series193.0ms

simplify75.0ms

prune73.0ms

localize14.0ms

rewrite58.0ms

series462.0ms

simplify88.0ms

prune99.0ms

localize20.0ms

rewrite49.0ms

series450.0ms

simplify90.0ms

prune136.0ms

regimes80.0ms

bsearch14.0ms

simplify2.0ms

end0.0ms

sample265.0ms

Profiling