Details

sample15.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.012207%

Guaranteed chance to sample good point: 99.99593%

Results

7.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series25.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	460	585
1	1938	554
2	5002	551

prune128.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Merged error: 0b

Counts

71 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
6.5b	(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
7.7b	(sqrt (+ (pow x 3) (pow 1.0 3)))
9.4b	(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

143×	`*-un-lft-identity`
114×	`sqrt-prod`
84×	`times-frac`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
44×	`distribute-lft-out`
32×	`unpow-prod-down` `cube-prod`
15×	`associate-/l*`
10×	`associate-/r*`
8×	`add-exp-log` `sqrt-div` `sum-cubes` `add-cbrt-cube`
6×	`pow1`
5×	`flip3-+` `flip-+`
4×	`associate-/r/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `associate-/l/`
1×	`sqrt-undiv`

Counts

4 → 176

Calls

4 calls:

34.0ms	(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
23.0ms	(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
11.0ms	(sqrt (+ (pow x 3) (pow 1.0 3)))
5.0ms	(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
7.0ms	(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
4.0ms	(sqrt (+ (pow x 3) (pow 1.0 3)))
4.0ms	(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	699	3257
1	3047	3043
2	5002	3032

prune380.0ms

Filtered

104 candidates to 188 candidates (-80.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	188	3	191

Merged error: 0b

Counts

191 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(/ x (+ 1.0 (log (exp (sqrt (+ x 1.0))))))
0.0b	(exp (sqrt (+ x 1.0)))
1.5b	(log (exp (sqrt (+ x 1.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
15×	`times-frac`
14×	`exp-prod`
12×	`sqrt-prod` `log-pow`
11×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*` `add-log-exp`
3×	`log-prod` `associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 87

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(/ x (+ 1.0 (log (exp (sqrt (+ x 1.0))))))
4.0ms	(exp (sqrt (+ x 1.0)))
4.0ms	(log (exp (sqrt (+ x 1.0))))

series29.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
15.0ms	(/ x (+ 1.0 (log (exp (sqrt (+ x 1.0))))))
7.0ms	(exp (sqrt (+ x 1.0)))
4.0ms	(log (exp (sqrt (+ x 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	580	891
1	2495	824
2	5002	812

prune182.0ms

Filtered

73 candidates to 99 candidates (-35.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	99	3	102

Merged error: 0b

Counts

102 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
0.0b	(sqrt (+ x 1.0))
4.3b	(- (- (* 1.0 1.0) x) 1.0)
4.3b	(- 1.0 (sqrt (+ x 1.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`associate-l`
16×	`times-frac`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`difference-of-squares`
7×	`pow1`
6×	`associate-r` `sqrt-prod` `distribute-lft-out--`
5×	`sub-neg` `flip3--` `flip--`
4×	`diff-log`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `associate-*r/` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate--l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

18.0ms	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(- (- (* 1.0 1.0) x) 1.0)
6.0ms	(- 1.0 (sqrt (+ x 1.0)))

series16.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
3.0ms	(sqrt (+ x 1.0))
1.0ms	(- (- (* 1.0 1.0) x) 1.0)
5.0ms	(- 1.0 (sqrt (+ x 1.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	503	940
1	2155	875
2	5001	866

prune166.0ms

Filtered

82 candidates to 112 candidates (-36.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	112	3	115

Merged error: 0b

Counts

115 → 3

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.0b

bsearch15.0ms

Steps

Iters	Range		Point
9	0.05542000641073973	11806.685469302465	0.8795243452021285

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	14
1	20	14

end0.0ms

sample353.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.012207%

Guaranteed chance to sample good point: 99.99593%

Results

223.0ms	7995×	body	80	valid
1.0ms	5×	body	1280	valid

Details

sample15.0ms

simplify3.0ms

prune2.0ms

localize5.0ms

rewrite17.0ms

series25.0ms

simplify48.0ms

prune128.0ms

localize16.0ms

rewrite82.0ms

series37.0ms

simplify86.0ms

prune380.0ms

localize11.0ms

rewrite23.0ms

series29.0ms

simplify55.0ms

prune182.0ms

localize9.0ms

rewrite36.0ms

series16.0ms

simplify57.0ms

prune166.0ms

regimes35.0ms

bsearch15.0ms

simplify1.0ms

end0.0ms

sample353.0ms

Profiling