Details

sample74.0ms

Algorithm

intervals

Results

35.0ms	878×	body	80	nan
13.0ms	296×	body	80	valid

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	76	10
2	211	10
3	530	10
4	1065	10
5	2198	10
6	3794	10
7	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
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)))))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 122

Calls

4 calls:

45.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
42.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
62.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
16.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
73.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
179.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
142.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	860	1389
1	3774	1282
2	5001	1276

prune613.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

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

rewrite443.0ms

Algorithm

rewrite-expression-head

Rules

795×	`times-frac`
608×	`add-sqr-sqrt`
452×	`sqrt-prod`
440×	`*-un-lft-identity`
346×	`add-cube-cbrt`
210×	`associate-l`
94×	`difference-of-squares`
47×	`distribute-lft-out--`
22×	`associate-/l*`
21×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `associate-/r*`
8×	`unswap-sqr`
6×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `associate-r` `flip--`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-*l/` `flip-+`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 533

Calls

4 calls:

23.0ms	(sqrt (- a (/ 1.0 3.0)))
46.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
112.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
219.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (- a (/ 1.0 3.0)))
159.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
196.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
165.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify96.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1709	6779
1	5001	6508

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize14.0ms

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 1)) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))))))
0.2b	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
0.3b	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `sqrt-prod`
15×	`associate-l`
13×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
11×	`pow1`
9×	`associate-r`
6×	`flip3--` `times-frac` `sqrt-div` `associate-*l/` `flip--` `difference-of-squares`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-/r/` `-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-unprod` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 115

Calls

4 calls:

24.0ms	(sqrt (- a (/ 1.0 3.0)))
46.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 1)) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))))))
19.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
45.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

series447.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (- a (/ 1.0 3.0)))
138.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 1)) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))))))
184.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
85.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

simplify88.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	761	1409
1	3381	1290
2	5001	1276

prune580.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize14.0ms

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

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
343×	`add-sqr-sqrt`
259×	`*-un-lft-identity`
258×	`sqrt-prod`
205×	`add-cube-cbrt`
54×	`difference-of-squares`
36×	`associate-/l*`
27×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3--` `flip--`
9×	`div-inv`
7×	`pow1`
6×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

4 → 362

Calls

4 calls:

23.0ms	(sqrt (- a (/ 1.0 3.0)))
46.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 1)) (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))))
41.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
23.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (- a (/ 1.0 3.0)))
146.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 1)) (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))))
187.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
84.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1398	5204
1	5001	4922

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes147.0ms

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	22	13
1	22	13

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	27420×	body	80	nan
403.0ms	9180×	body	80	valid