Details

sample73.0ms

Algorithm

intervals

Results

30.0ms	896×	body	80	nan
10.0ms	281×	body	80	valid

simplify96.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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)))
0.1b	(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)))))

rewrite140.0ms

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×	`frac-times` `associate-/r*` `associate-/r/` `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 → 114

Calls

4 calls:

47.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
11.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
61.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
16.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
69.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
175.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
140.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	823	1338
1	3607	1238
2	5002	1238

prune370.0ms

Pruning

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

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `associate-r`
9×	`associate-l`
8×	`associate-*r/`
6×	`flip3--` `times-frac` `flip--`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `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` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

38.0ms	(* 9.0 (- a (/ 1.0 3.0)))
88.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
11.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
23.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 9.0 (- a (/ 1.0 3.0)))
115.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
70.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
189.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	744	1044
1	3484	958
2	5001	958

prune289.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 1.0 rand) (sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.5b	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

67×	`pow1`
41×	`pow-prod-down`
40×	`add-sqr-sqrt`
36×	`sqrt-div`
32×	`associate-*r/`
28×	`sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
20×	`sqrt-pow1` `pow1/2`
19×	`associate-r`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt` `flip3--` `flip--`
13×	`associate-l`
11×	`prod-exp` `cbrt-unprod`
8×	`frac-times` `associate-/r/` `pow-prod-up` `unswap-sqr`
7×	`sqrt-unprod`
6×	`times-frac` `pow-sqr`
4×	`associate-l/` `associate-/r` `add-log-exp` `difference-of-squares`
3×	`*-commutative`
2×	`cbrt-undiv` `pow-plus` `div-exp` `distribute-lft-out--`
1×	`pow2` `frac-2neg` `swap-sqr` `clear-num` `rem-square-sqrt` `div-inv` `associate-/l*`

Counts

4 → 153

Calls

4 calls:

109.0ms	(/ (* 1.0 rand) (sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
43.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
42.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
109.0ms	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(/ (* 1.0 rand) (sqrt (* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
86.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
85.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
99.0ms	(* (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	656	1552
1	3091	1360
2	5001	1316

prune426.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite342.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
132×	`add-sqr-sqrt`
102×	`sqrt-prod`
89×	`*-un-lft-identity`
59×	`add-cube-cbrt`
28×	`difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`flip3--` `associate-l` `flip--` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`flip3-+` `flip-+`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

4 → 193

Calls

4 calls:

9.0ms	(- a (/ 1.0 3.0))
16.0ms	(sqrt (- a (/ 1.0 3.0)))
272.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
36.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- a (/ 1.0 3.0))
35.0ms	(sqrt (- a (/ 1.0 3.0)))
149.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
227.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify103.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	995	2600
1	4426	2434
2	5001	2434

prune488.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes92.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b 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	20	18
1	20	18

end0.0ms

sample2.0s

Algorithm

intervals

Results

840.0ms	28112×	body	80	nan
310.0ms	9128×	body	80	valid