Details

analyze3.0ms

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

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 28.2b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

27.0b

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `*-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` `flip-+_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify72.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4818	91
1	4818	91

prune20.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	10	6	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	7	17

Merged error: 0.1b

Counts

17 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
27.0b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.0b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-pow1_binary64`
71×	`pow1_binary64`
33×	`sqrt-prod_binary64`
32×	`sqrt-div_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`pow-prod-down_binary64`
22×	`pow1/2_binary64`
20×	`associate-*r/_binary64`
14×	`pow-prod-up_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `swap-sqr_binary64` `flip-+_binary64`
8×	`pow-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` `frac-times_binary64`
2×	`associate-*l/_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 → 124

Calls

4 calls:

6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
4.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
7.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
4.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4895	929
1	4895	929

prune45.0ms

Filtered

70 candidates to 136 candidates (-94.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	136	7	143

Merged error: 0.1b

Counts

143 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) 3) (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 3)
27.0b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.0b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

104×	`sqrt-prod_binary64`
66×	`add-sqr-sqrt_binary64`
46×	`sqrt-div_binary64`
29×	`unpow-prod-down_binary64` `cube-prod_binary64`
26×	`associate-l_binary64`
24×	`unswap-sqr_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`associate-*r/_binary64`
17×	`pow1_binary64`
16×	`sqrt-pow1_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`pow-pow_binary64` `cube-div_binary64`
7×	`add-cbrt-cube_binary64`
5×	`pow1/2_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `prod-exp_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `associate-*l/_binary64` `cube-mult_binary64`
1×	`cbrt-unprod_binary64` `sqrt-pow2_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `rem-cube-cbrt_binary64` `*-commutative_binary64`

Counts

4 → 155

Calls

4 calls:

20.0ms	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) 3) (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
9.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 3)
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) 3) (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
32.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 3)
4.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
4.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4833	1797
1	4833	1797

prune53.0ms

Filtered

83 candidates to 167 candidates (-101.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	167	7	174

Merged error: 0.1b

Counts

174 → 7

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify34.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4888	133
1	4888	133

prune13.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	23	9	32

Merged error: 0.0b

Counts

32 → 9

regimes32.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.0b

bsearch14.0ms

Steps

Iters	Range		Point
12	-2.0277624387170858e-307	5.379442571176017e-265	-9.3091014976277e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	21
1	50	21

end0.0ms

sample263.0ms

Algorithm

intervals

Results

176.0ms

8000×

body

valid

Details

analyze3.0ms

sample10.0ms

simplify5.0ms

prune4.0ms

localize4.0ms

rewrite5.0ms

series4.0ms

simplify72.0ms

prune20.0ms

localize7.0ms

rewrite40.0ms

series23.0ms

simplify88.0ms

prune45.0ms

localize9.0ms

rewrite47.0ms

series45.0ms

simplify74.0ms

prune53.0ms

localize4.0ms

rewrite6.0ms

series4.0ms

simplify34.0ms

prune13.0ms

regimes32.0ms

bsearch14.0ms

simplify2.0ms

end0.0ms

sample263.0ms

Profiling