Details

sample66.0ms

Algorithm

intervals

Results

25.0ms	829×	body	80	nan
10.0ms	294×	body	80	valid

simplify104.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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))))

rewrite176.0ms

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:

48.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
63.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
19.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
40.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
169.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
136.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
66.0ms	(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

prune399.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

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

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 183

Calls

4 calls:

47.0ms	(* 9.0 (- a (/ 1.0 3.0)))
92.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
21.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
41.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 9.0 (- a (/ 1.0 3.0)))
109.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
185.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
65.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify59.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1157	3007
1	5001	2366

prune371.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
6.7b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
79×	`add-cube-cbrt`
78×	`prod-diff`
64×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
9×	`associate-r/` `associate-l*`
8×	`div-inv`
6×	`flip3--` `sqrt-div` `prod-exp` `flip--` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down`
2×	`frac-times` `sub-neg` `sqrt-pow1` `associate-l/` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 188

Calls

4 calls:

48.0ms	(* 9.0 (- a (/ 1.0 3.0)))
22.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
41.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
90.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* 9.0 (- a (/ 1.0 3.0)))
189.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
153.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify129.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1106	2987
1	4932	2299
2	5001	2299

prune386.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
6.7b	(* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

319×	`times-frac`
230×	`add-sqr-sqrt`
190×	`sqrt-prod`
152×	`*-un-lft-identity`
106×	`add-cube-cbrt`
96×	`associate-r`
46×	`difference-of-squares`
27×	`add-exp-log` `add-cbrt-cube`
23×	`distribute-lft-out--`
21×	`div-inv`
16×	`associate-*l/`
14×	`flip3--` `flip--`
10×	`cbrt-undiv` `div-exp` `frac-add` `associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`frac-times` `sqrt-div` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`associate-*r/` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `fma-def` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `associate-/l/` `distribute-lft-out`

Counts

4 → 304

Calls

4 calls:

24.0ms	(sqrt (- a (/ 1.0 3.0)))
24.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
33.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
119.0ms	(* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (- a (/ 1.0 3.0)))
178.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
223.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
187.0ms	(* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1442	4247
1	5001	3948

prune833.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes80.0ms

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	19	14
1	19	14

end0.0ms

sample1.9s

Algorithm

intervals

Results

829.0ms	26921×	body	80	nan
314.0ms	9158×	body	80	valid