Details

sample99.0ms

Algorithm

intervals

Results

54.0ms	791×	body	80	nan
21.0ms	289×	body	80	valid

simplify92.0ms

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

localize10.0ms

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)))))

rewrite79.0ms

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:

25.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
35.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
8.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
72.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
180.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
162.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

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

prune351.0ms

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	(+ 1.0 (/ (* 1.0 rand) (sqrt (* 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)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

7.0ms	(+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
47.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
9.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
138.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
189.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	693	1082
1	3160	991
2	5002	991

prune271.0ms

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	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 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)))))
6.5b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt` `associate-*l/`
14×	`flip3--` `flip--`
11×	`*-un-lft-identity`
10×	`associate-r` `frac-add`
9×	`pow1` `add-cube-cbrt` `times-frac` `associate-*r/`
6×	`frac-times` `sqrt-div` `associate-l` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r*` `sqrt-prod` `associate-/r/`
2×	`sqrt-pow1` `pow-prod-down` `div-inv` `difference-of-squares`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow1/2` `clear-num` `sum-log` `-commutative` `flip-+` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

10.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
9.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
50.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
197.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
163.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	887	1538
1	4258	1371
2	5003	1371

prune320.0ms

Pruning

5 alts after pruning (4 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)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
0.2b	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
6.5b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log` `add-cbrt-cube`
30×	`add-sqr-sqrt`
16×	`associate-r` `associate-*l/`
14×	`flip3--` `*-un-lft-identity` `prod-exp` `flip--` `cbrt-unprod`
13×	`sqrt-prod`
12×	`associate-l`
10×	`pow1` `add-cube-cbrt` `frac-add`
9×	`associate-*r/`
8×	`cbrt-undiv` `div-exp`
6×	`frac-times` `sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`times-frac` `pow-prod-down` `associate-/r/` `difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `*-commutative` `div-inv` `distribute-lft-out--`
1×	`+-commutative` `frac-2neg` `flip3-+` `sqrt-unprod` `clear-num` `associate-/r` `sum-log` `flip-+` `distribute-lft-out` `associate-/l`

Counts

4 → 118

Calls

4 calls:

10.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
11.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
25.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
53.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
242.0ms	(/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
92.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
197.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	950	1843
1	5001	1623

prune348.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes57.0ms

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	13
1	19	13

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.8s	27512×	body	80	nan
662.0ms	9111×	body	80	valid