Details

sample62.0ms

Algorithm

intervals

Results

28.0ms	732×	body	80	nan
10.0ms	286×	body	80	valid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	10
1	72	10
2	192	10
3	437	10
4	816	10
5	1578	10
6	2764	10
7	5002	10

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
137×	`sqrt-prod`
121×	`times-frac`
105×	`*-un-lft-identity`
94×	`associate-l`
81×	`add-cube-cbrt`
62×	`associate-r`
36×	`associate-/r*`
26×	`associate-*l/`
20×	`difference-of-squares`
16×	`unswap-sqr`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1` `*-commutative`
10×	`distribute-lft-out--`
8×	`associate-*r/`
6×	`flip3--` `sqrt-div` `flip--` `associate-/l*`
4×	`frac-times` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `div-exp` `clear-num` `div-inv` `distribute-lft-out`
1×	`pow1/2`

Counts

4 → 257

Calls

4 calls:

42.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
30.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
14.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
185.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
149.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1091	2522
1	5001	2414

prune767.0ms

Filtered

269 candidates to 209 candidates (77.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	263	6	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	264	6	270

Merged error: 0.0b

Counts

270 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.2b	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

273×	`add-sqr-sqrt`
232×	`times-frac`
210×	`sqrt-prod`
154×	`*-un-lft-identity`
151×	`associate-r`
120×	`add-cube-cbrt`
108×	`associate-l`
36×	`unswap-sqr`
35×	`*-commutative`
32×	`difference-of-squares`
18×	`associate-/r*`
16×	`distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/l*`
11×	`pow1`
8×	`associate-*r/`
6×	`flip3--` `flip--`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `div-exp` `associate-*l/` `associate-/r/`
1×	`frac-2neg` `pow1/2` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 352

Calls

4 calls:

9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
67.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
25.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 9.0 (- a (/ 1.0 3.0)))
127.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
194.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify76.0ms

Algorithm

egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1340	4158
1	5001	4069

prune935.0ms

Filtered

364 candidates to 250 candidates (68.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	362	2	364
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	365	5	370

Merged error: 0.0b

Counts

370 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.0b	(* (- a (/ 1.0 3.0)) (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

566×	`add-sqr-sqrt`
522×	`associate-r`
469×	`times-frac`
439×	`sqrt-prod`
307×	`*-un-lft-identity`
243×	`add-cube-cbrt`
217×	`associate-l`
83×	`unswap-sqr`
72×	`associate-/r*`
71×	`*-commutative`
66×	`frac-times`
62×	`difference-of-squares`
50×	`associate-/l*`
41×	`associate-*r/`
38×	`flip3--` `flip--`
31×	`distribute-lft-out--`
20×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
6×	`sqrt-div` `prod-exp` `cbrt-unprod`
5×	`clear-num`
4×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-/r/` `add-log-exp`
3×	`pow-prod-down` `un-div-inv`
2×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `associate-*l/` `div-inv`
1×	`pow1/2`

Counts

4 → 672

Calls

4 calls:

9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
22.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
88.0ms	(* (- a (/ 1.0 3.0)) (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 9.0 (- a (/ 1.0 3.0)))
202.0ms	(/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
78.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
169.0ms	(* (- a (/ 1.0 3.0)) (/ (* rand 1.0) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

684 → 684

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2134	7732
1	5001	7642

prune1.9s

Filtered

684 candidates to 467 candidates (68.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	681	3	684
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	685	4	689

Merged error: 0b

Counts

689 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
9.0b	(/ (* 1.0 (- a (/ 1.0 3.0))) (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

1902×	`times-frac`
1523×	`add-sqr-sqrt`
950×	`*-un-lft-identity`
810×	`sqrt-prod`
722×	`add-cube-cbrt`
684×	`associate-r`
342×	`associate-l`
228×	`difference-of-squares`
115×	`unswap-sqr`
114×	`*-commutative` `distribute-lft-out--`
64×	`associate-/r*`
51×	`associate-/l*`
26×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
18×	`div-inv`
10×	`associate-*r/`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`sqrt-div` `associate-/l/`
5×	`flip3--` `flip--`
4×	`add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow-prod-down`
1×	`pow1/2`

Counts

4 → 1134

Calls

4 calls:

10.0ms	(* 9.0 (- a (/ 1.0 3.0)))
19.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
51.0ms	(/ (* 1.0 (- a (/ 1.0 3.0))) (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

series461.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* 9.0 (- a (/ 1.0 3.0)))
159.0ms	(/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand)
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
177.0ms	(/ (* 1.0 (- a (/ 1.0 3.0))) (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) rand))

simplify196.0ms

Algorithm

egg-herbie

Counts

1146 → 1146

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5001	19972

prune3.2s

Filtered

1146 candidates to 754 candidates (65.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1145	1	1146
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	1147	3	1150

Merged error: 0b

Counts

1150 → 3

regimes58.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	18	13
2	18	13

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	27968×	body	80	nan
337.0ms	9112×	body	80	valid