Details

sample65.0ms

Algorithm

intervals

Results

29.0ms	872×	body	80	nan
10.0ms	299×	body	80	valid

simplify102.0ms

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: 0.1b

localize13.0ms

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))))

rewrite57.0ms

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:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
183.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
146.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify92.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (78.0ms)

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

prune402.0ms

Pruning

8 alts after pruning (8 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))))

rewrite68.0ms

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)))
14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
19.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 9.0 (- a (/ 1.0 3.0)))
118.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
186.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify50.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1157	3007
1	5001	2366

prune352.0ms

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))))
6.3b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite71.0ms

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:

14.0ms	(* 9.0 (- a (/ 1.0 3.0)))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
19.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series468.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* 9.0 (- a (/ 1.0 3.0)))
191.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
73.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
160.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify117.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (24.0ms)

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

prune385.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 rand) (sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0))))))
0.4b	(sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0)))))
6.3b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0)))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 93

Calls

3 calls:

8.0ms	(/ (* 1.0 rand) (sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0))))))
3.0ms	(sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0)))))
16.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0)))))))

series345.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(/ (* 1.0 rand) (sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0))))))
51.0ms	(sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0)))))
170.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (+ (* 9.0 a) (* 9.0 (- (/ 1.0 3.0)))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	631	1221
1	2903	1081
2	5002	1069

prune286.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	15
1	32	15
2	33	15
3	33	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

901.0ms	27357×	body	80	nan
321.0ms	9192×	body	80	valid