Details

Time bar (total: 6.2s)

sample64.0ms

Algorithm
intervals
Results
28.0ms925×body80nan
10.0ms300×body80valid

simplify105.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02710
17610
221110
353010
4106510
5219810
6379410
7500110

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

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

rewrite61.0ms

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)))
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)))))
22.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
178.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
142.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
74.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify94.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08601391
137681282
250021276

prune391.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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

rewrite66.0ms

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:
13.0ms
(* 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)))))
18.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series434.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* 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)))))))
198.0ms
(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
74.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify53.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011573007
150012366

prune380.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- a (/ 1.0 3.0)))
0.0b
(+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (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))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
163×times-frac
128×add-sqr-sqrt
102×sqrt-prod
90×*-un-lft-identity
60×add-cube-cbrt
26×difference-of-squares
15×add-exp-log add-cbrt-cube
13×distribute-lft-out--
11×div-inv
10×associate-/l*
9×associate-/r*
7×pow1
6×associate-*l* add-log-exp
5×cbrt-undiv flip3-- div-exp flip--
4×expm1-log1p-u frac-times flip3-+ sqrt-div associate-*r* flip-+ log1p-expm1-u
3×fma-def
2×associate-*r/ associate-*l/ prod-exp associate-/r/ cbrt-unprod distribute-lft-out
1×+-commutative distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down clear-num sum-log *-commutative associate-/l/ unswap-sqr
Counts
4 → 201
Calls
4 calls:
9.0ms
(sqrt (- a (/ 1.0 3.0)))
32.0ms
(+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
36.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
19.0ms
(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series575.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (- a (/ 1.0 3.0)))
144.0ms
(+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))
154.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
234.0ms
(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify113.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
010382780
146132596
250012593

prune564.0ms

Pruning

7 alts after pruning (6 fresh and 1 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 (fma (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))) 1.0)))
0.1b
(fma (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))) 1.0)
0.2b
(/ rand (sqrt (- a (/ 1.0 3.0))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
36×*-un-lft-identity
33×times-frac
30×sqrt-prod
24×add-cube-cbrt
13×add-exp-log
12×difference-of-squares
11×add-cbrt-cube
10×pow1
9×associate-/r*
6×associate-*l* distribute-lft-out--
5×prod-exp fma-udef
4×distribute-rgt-in expm1-log1p-u distribute-lft-in sqrt-div log1p-expm1-u add-log-exp
3×flip3-- pow-prod-down flip-- cbrt-unprod associate-/l*
2×associate-*l/ associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 1-exp div-exp associate-*r* clear-num *-commutative div-inv
Counts
4 → 115
Calls
4 calls:
9.0ms
(sqrt (- a (/ 1.0 3.0)))
10.0ms
(* (- a (/ 1.0 3.0)) (* 1 (fma (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))) 1.0)))
1.0ms
(fma (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))) 1.0)
9.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (- a (/ 1.0 3.0)))
146.0ms
(* (- a (/ 1.0 3.0)) (* 1 (fma (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))) 1.0)))
142.0ms
(fma (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))) 1.0)
83.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))

simplify65.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06241243
123861104
250011098

prune347.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes100.0ms

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)

IterNodesCost
01711
11711

end0.0ms

sample1.7s

Algorithm
intervals
Results
817.0ms27139×body80nan
300.0ms9110×body80valid