Details

sample61.0ms

Algorithm

intervals

Results

27.0ms	882×	body	80	nan
10.0ms	303×	body	80	valid

simplify93.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

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

rewrite85.0ms

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:

30.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
36.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
187.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
155.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	823	1340
1	3601	1238
2	5002	1238

prune387.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

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

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

795×	`times-frac`
608×	`add-sqr-sqrt`
452×	`sqrt-prod`
440×	`*-un-lft-identity`
346×	`add-cube-cbrt`
210×	`associate-l`
94×	`difference-of-squares`
47×	`distribute-lft-out--`
22×	`associate-/l*`
21×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `associate-/r*`
8×	`unswap-sqr`
6×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `associate-r` `flip--`
4×	`frac-times` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `associate-*l/` `flip-+`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 525

Calls

4 calls:

10.0ms	(sqrt (- a (/ 1.0 3.0)))
27.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
92.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
22.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series648.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (- a (/ 1.0 3.0)))
154.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
225.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
232.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify92.0ms

Algorithm

egg-herbie

Counts

537 → 537

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1672	6723
1	5001	6455

prune1.4s

Filtered

537 candidates to 325 candidates (60.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize13.0ms

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

10.0ms	(sqrt (- a (/ 1.0 3.0)))
30.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 1) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))))))
10.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
27.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

series506.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (- a (/ 1.0 3.0)))
168.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 1) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))))))
201.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
91.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	729	1292
1	3314	1177
2	5002	1173

prune345.0ms

Filtered

119 candidates to 91 candidates (76.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.2b	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
0.3b	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))
6.5b	(* (* (- a (/ 1.0 3.0)) 1.0) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

10.0ms	(sqrt (- a (/ 1.0 3.0)))
11.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
29.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))
56.0ms	(* (* (- a (/ 1.0 3.0)) 1.0) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (- a (/ 1.0 3.0)))
197.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
93.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))
213.0ms	(* (* (- a (/ 1.0 3.0)) 1.0) (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))))

simplify78.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	714	1254
1	3332	1084
2	5002	1080

prune309.0ms

Filtered

125 candidates to 87 candidates (69.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes67.0ms

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	18	13
1	18	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

849.0ms	27637×	body	80	nan
309.0ms	9143×	body	80	valid