Details

sample19.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.012207%

Guaranteed chance to sample good point: 99.991861%

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: 0.1b

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))
0.1b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite18.0ms

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))
8.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series24.0ms

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))))

simplify47.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (40.0ms)

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

prune131.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
232×	`sqrt-prod`
192×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 317

Calls

4 calls:

8.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
9.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
20.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
15.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
29.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
16.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify127.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1126	5982
1	4661	5345
2	5002	5337

prune533.0ms

Filtered

147 candidates to 329 candidates (-123.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	329	4	333

Merged error: 0b

Counts

333 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
7.0b	(/ (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)))
10.5b	(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite83.0ms

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:

38.0ms	(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
20.0ms	(/ (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))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 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))))

simplify92.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (59.0ms)

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

prune378.0ms

Filtered

104 candidates to 188 candidates (-80.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	188	4	192

Merged error: 0b

Counts

192 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 132

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
27.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
15.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	856	1494
1	4169	1377
2	5002	1353

prune199.0ms

Filtered

94 candidates to 144 candidates (-53.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	144	4	148

Merged error: 0b

Counts

148 → 4

regimes85.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample378.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.012207%

Guaranteed chance to sample good point: 99.991861%

Results

238.0ms	7996×	body	80	valid
1.0ms	4×	body	1280	valid

Details

sample19.0ms

simplify3.0ms

prune2.0ms

localize5.0ms

rewrite18.0ms

series24.0ms

simplify47.0ms

prune131.0ms

localize8.0ms

rewrite61.0ms

series70.0ms

simplify127.0ms

prune533.0ms

localize18.0ms

rewrite83.0ms

series34.0ms

simplify92.0ms

prune378.0ms

localize7.0ms

rewrite39.0ms

series50.0ms

simplify96.0ms

prune199.0ms

regimes85.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample378.0ms

Profiling