Details

sample71.0ms

Algorithm

intervals

Results

29.0ms	796×	body	80	nan
15.0ms	295×	body	80	valid

simplify101.0ms

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

localize11.0ms

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

rewrite62.0ms

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:

11.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
22.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
15.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
11.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
74.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
181.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
142.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify97.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (79.0ms)

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

prune432.0ms

Pruning

10 alts after pruning (10 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)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.2b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite74.0ms

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:

14.0ms	(* 9.0 (- a (/ 1.0 3.0)))
15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
19.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
15.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 9.0 (- a (/ 1.0 3.0)))
119.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
196.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1157	3007
1	5001	2366

prune399.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

165×	`distribute-rgt-in` `distribute-lft-in`
156×	`prod-diff`
153×	`add-sqr-sqrt`
150×	`*-un-lft-identity`
146×	`add-cube-cbrt`
113×	`times-frac`
17×	`pow1`
16×	`add-exp-log` `add-cbrt-cube`
14×	`associate-*r/`
13×	`div-inv`
12×	`associate-l`
7×	`pow-prod-down`
6×	`flip3--` `sqrt-prod` `flip--`
5×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `frac-times` `sub-neg` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-/r/` `-commutative` `difference-of-squares`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out` `associate-/l*` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 266

Calls

4 calls:

17.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))))))
35.0ms	(sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0)))))
16.0ms	(/ (* 1.0 rand) (sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))))
24.0ms	(* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))

series762.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))))))
121.0ms	(sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0)))))
313.0ms	(/ (* 1.0 rand) (sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))))
112.0ms	(* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1607	5313
1	5001	4473

prune466.0ms

Pruning

7 alts after pruning (7 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)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
93×	`times-frac`
72×	`*-un-lft-identity`
63×	`sqrt-prod`
54×	`add-cube-cbrt`
36×	`associate-r`
28×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`difference-of-squares`
10×	`unswap-sqr`
9×	`pow1` `associate-/r*` `distribute-lft-out--`
6×	`flip3--` `sqrt-div` `flip--`
5×	`cbrt-undiv` `frac-times` `div-exp` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-r/` `associate-l/` `flip-+` `div-inv` `associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 194

Calls

4 calls:

9.0ms	(sqrt (- a (/ 1.0 3.0)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
10.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
26.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series509.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (- a (/ 1.0 3.0)))
153.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))))
84.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
234.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1070	2186
1	4960	2047
2	5001	2047

prune684.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes92.0ms

Accuracy

0% (0.1b 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	17	11
1	17	11

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.0s	27219×	body	80	nan
357.0ms	9136×	body	80	valid