Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample12.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.0b	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.2b	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`distribute-lft-out_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `sqrt-prod_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 61

Calls

3 calls:

3.0ms	(sqrt.f64 (+.f64 x 1.0))
6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
8.0ms	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

series38.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(sqrt.f64 (+.f64 x 1.0))
6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
27.0ms	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

simplify27.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4963	1021
1	4963	1021

prune91.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 0b

Counts

71 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.2b	(/.f64 x (cbrt.f64 (pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3)))
0.2b	(pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3)
7.3b	(cbrt.f64 (pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64` `cbrt-prod_binary64`
51×	`times-frac_binary64`
44×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
24×	`unpow-prod-down_binary64` `cube-prod_binary64`
17×	`associate-/r*_binary64`
13×	`distribute-lft-out_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `cube-div_binary64` `unpow3_binary64` `cube-mult_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3-+_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 149

Calls

4 calls:

6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
11.0ms	(/.f64 x (cbrt.f64 (pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3)))
7.0ms	(pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3)
7.0ms	(cbrt.f64 (pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3))

series56.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
22.0ms	(/.f64 x (cbrt.f64 (pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3)))
22.0ms	(pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3)
6.0ms	(cbrt.f64 (pow.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))) 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5038	2597

prune136.0ms

Filtered

93 candidates to 161 candidates (-73.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	161	5	166

Merged error: 0b

Counts

166 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 x) (*.f64 (cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) (cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))))
0.8b	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
0.8b	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
0.8b	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div_binary64`
17×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `add-exp-log_binary64` `flip-+_binary64`
8×	`associate-/r/_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `frac-times_binary64`
3×	`distribute-lft-out_binary64` `pow1/3_binary64`
2×	`cbrt-undiv_binary64` `associate-r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`associate-/r*_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 77

Calls

4 calls:

17.0ms	(/.f64 (sqrt.f64 x) (*.f64 (cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) (cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))))
6.0ms	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
6.0ms	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
6.0ms	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.4s	(/.f64 (sqrt.f64 x) (*.f64 (cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) (cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))))
31.0ms	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
29.0ms	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
31.0ms	(cbrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5169	3599

prune251.0ms

Filtered

77 candidates to 89 candidates (-15.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	89	5	94

Merged error: 0b

Counts

94 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))
0.0b	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.2b	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
3.7b	(exp.f64 (log.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
36×	`log-prod_binary64` `times-frac_binary64`
30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`exp-sum_binary64`
11×	`distribute-lft-out_binary64`
9×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
4×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64` `exp-prod_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`rem-log-exp_binary64` `log-pow_binary64` `div-exp_binary64` `log-div_binary64`
1×	`cbrt-undiv_binary64` `rem-exp-log_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 105

Calls

4 calls:

8.0ms	(log.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))
6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
8.0ms	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
10.0ms	(exp.f64 (log.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(log.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))
6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
23.0ms	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
26.0ms	(exp.f64 (log.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4967	2646
1	4967	2646

prune143.0ms

Filtered

86 candidates to 117 candidates (-36.0%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	117	5	122

Merged error: 0b

Counts

122 → 5

regimes70.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

end0.0ms

sample304.0ms

Algorithm

intervals

Results

218.0ms	7998×	body	80	valid
0.0ms	2×	body	1280	valid

Details

analyze2.0ms

sample12.0ms

simplify5.0ms

prune2.0ms

localize5.0ms

rewrite18.0ms

series38.0ms

simplify27.0ms

prune91.0ms

localize8.0ms

rewrite37.0ms

series56.0ms

simplify57.0ms

prune136.0ms

localize12.0ms

rewrite37.0ms

series1.5s

simplify45.0ms

prune251.0ms

localize9.0ms

rewrite35.0ms

series116.0ms

simplify56.0ms

prune143.0ms

regimes70.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample304.0ms

Profiling