Details

sample78.0ms

Algorithm

intervals

Results

36.0ms	964×	body	80	nan
11.0ms	296×	body	80	valid

simplify104.0ms

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

prune3.0ms

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: 0.2b

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

rewrite120.0ms

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:

45.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
32.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
15.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
11.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
219.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
176.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
91.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1082	2522
1	5001	2407

prune679.0ms

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

localize11.0ms

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

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

406×	`times-frac`
316×	`add-sqr-sqrt`
237×	`*-un-lft-identity`
210×	`sqrt-prod`
201×	`add-cube-cbrt`
100×	`associate-r`
65×	`associate-/r*`
51×	`associate-l`
32×	`associate-/r/` `difference-of-squares`
21×	`associate-/l*`
17×	`unswap-sqr`
16×	`*-commutative` `distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/`
6×	`flip3--` `flip--`
5×	`div-inv`
4×	`distribute-rgt-in` `frac-times` `distribute-rgt-out` `distribute-lft-in` `sqrt-div` `add-log-exp`
3×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `flip-+`
2×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `associate-*l/` `distribute-rgt1-in` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`pow1/2` `distribute-lft-out`

Counts

4 → 371

Calls

4 calls:

10.0ms	(* 9.0 (- a (/ 1.0 3.0)))
76.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ rand (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) 1.0))))
29.0ms	(/ rand (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) 1.0))
14.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 9.0 (- a (/ 1.0 3.0)))
154.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ rand (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) 1.0))))
225.0ms	(/ rand (/ (sqrt (* 9.0 (- a (/ 1.0 3.0)))) 1.0))
92.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify94.0ms

Algorithm

egg-herbie

Counts

383 → 383

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1670	4446
1	5002	4241

prune1.1s

Filtered

383 candidates to 278 candidates (72.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	380	3	383
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	383	6	389

Merged error: 0.0b

Counts

389 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt 9.0)) rand)

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

553×	`times-frac`
516×	`add-sqr-sqrt`
326×	`sqrt-prod`
319×	`*-un-lft-identity`
248×	`associate-l`
245×	`add-cube-cbrt`
72×	`difference-of-squares`
39×	`associate-/l*`
37×	`associate-r`
36×	`distribute-lft-out--`
34×	`unswap-sqr`
26×	`associate-*l/`
21×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
12×	`*-commutative` `div-inv` `associate-/l/`
9×	`pow1`
5×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod`
4×	`frac-times` `sqrt-div` `add-log-exp`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-*r/` `pow-prod-down` `associate-/r/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

4 → 474

Calls

4 calls:

8.0ms	(sqrt (- a (/ 1.0 3.0)))
108.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))))
31.0ms	(/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))
10.0ms	(* (/ 1.0 (sqrt 9.0)) rand)

series571.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (- a (/ 1.0 3.0)))
173.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))))
280.0ms	(/ (* (/ 1.0 (sqrt 9.0)) rand) (sqrt (- a (/ 1.0 3.0))))
75.0ms	(* (/ 1.0 (sqrt 9.0)) rand)

simplify104.0ms

Algorithm

egg-herbie

Counts

486 → 486

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1633	6807
1	5001	6520

prune967.0ms

Filtered

486 candidates to 276 candidates (56.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	485	1	486
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	487	5	492

Merged error: 0b

Counts

492 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite941.0ms

Algorithm

rewrite-expression-head

Rules

6325×	`times-frac`
4217×	`sqrt-prod`
3503×	`add-sqr-sqrt`
2811×	`*-un-lft-identity`
2609×	`add-cube-cbrt`
598×	`associate-r`
594×	`associate-l`
199×	`unswap-sqr`
198×	`difference-of-squares`
105×	`div-inv`
99×	`*-commutative` `distribute-lft-out--`
95×	`associate-/r*`
59×	`associate-/l*`
36×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
17×	`associate-/l/`
9×	`pow1` `cbrt-undiv` `div-exp`
6×	`associate-*r/`
5×	`flip3--` `flip--`
4×	`frac-times` `distribute-rgt-out` `frac-2neg` `sqrt-div` `clear-num` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow-prod-down` `associate-*l/` `distribute-rgt1-in`
1×	`pow1/2` `prod-exp` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 2459

Calls

4 calls:

507.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ rand (sqrt (sqrt 9.0))) (/ (sqrt (* (sqrt 9.0) (- a (/ 1.0 3.0)))) 1.0))))
88.0ms	(/ (/ rand (sqrt (sqrt 9.0))) (/ (sqrt (* (sqrt 9.0) (- a (/ 1.0 3.0)))) 1.0))
12.0ms	(sqrt (* (sqrt 9.0) (- a (/ 1.0 3.0))))
5.0ms	(/ rand (sqrt (sqrt 9.0)))

series981.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ rand (sqrt (sqrt 9.0))) (/ (sqrt (* (sqrt 9.0) (- a (/ 1.0 3.0)))) 1.0))))
415.0ms	(/ (/ rand (sqrt (sqrt 9.0))) (/ (sqrt (* (sqrt 9.0) (- a (/ 1.0 3.0)))) 1.0))
150.0ms	(sqrt (* (sqrt 9.0) (- a (/ 1.0 3.0))))
117.0ms	(/ rand (sqrt (sqrt 9.0)))

simplify535.0ms

Algorithm

egg-herbie

Counts

2471 → 2471

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5001	57655

prune7.2s

Filtered

2471 candidates to 1441 candidates (58.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	2471	0	2471
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	2471	5	2476

Merged error: 0b

Counts

2476 → 5

regimes70.0ms

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	10
1	16	10

end0.0ms

sample1.9s

Algorithm

intervals

Results

917.0ms	27688×	body	80	nan
330.0ms	9141×	body	80	valid