Details

Time bar (total: 8.1s)

sample68.0ms

Algorithm
intervals
Results
28.0ms872×body80nan
9.0ms293×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:

0.0b
(* 9.0 (- a (/ 1.0 3.0)))
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)))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
94×*-un-lft-identity
92×add-cube-cbrt
80×times-frac
78×prod-diff
41×distribute-rgt-in distribute-lft-in
21×associate-*l*
13×add-exp-log add-cbrt-cube
11×pow1
9×associate-*r*
8×associate-*r/ sqrt-prod div-inv
6×sqrt-div
4×expm1-log1p-u flip3-- associate-/r* associate-/r/ flip-- log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv sub-neg sqrt-pow1 div-exp *-commutative difference-of-squares
1×frac-2neg pow1/2 associate-*l/ clear-num distribute-lft-out--
Counts
4 → 196
Calls
4 calls:
48.0ms
(* 9.0 (- a (/ 1.0 3.0)))
43.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
64.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
16.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* 9.0 (- a (/ 1.0 3.0)))
73.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
183.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
152.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify102.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
010572916
141522268
250012242

prune419.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite211.0ms

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:
88.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
49.0ms
(* 9.0 (- a (/ 1.0 3.0)))
43.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
21.0ms
(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series430.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
44.0ms
(* 9.0 (- a (/ 1.0 3.0)))
74.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
195.0ms
(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011573007
150012366

prune376.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ (fma a 9.0 (* 9.0 (/ (- (/ 1.0 (cbrt 3.0))) (* (cbrt 3.0) (cbrt 3.0))))) (* 9.0 (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (+ (- (/ 1.0 (cbrt 3.0))) (/ 1.0 (cbrt 3.0))))))))
1.0b
(/ 1.0 (cbrt 3.0))
1.0b
(/ 1.0 (cbrt 3.0))
1.0b
(/ 1.0 (cbrt 3.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
64×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×cbrt-prod
24×associate-/r*
12×add-exp-log sqrt-prod associate-/l*
9×add-cbrt-cube
4×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
2×sqrt-div associate-/r/
1×flip3-+ flip-+
Counts
4 → 166
Calls
4 calls:
10.0ms
(/ 1.0 (sqrt (+ (fma a 9.0 (* 9.0 (/ (- (/ 1.0 (cbrt 3.0))) (* (cbrt 3.0) (cbrt 3.0))))) (* 9.0 (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (+ (- (/ 1.0 (cbrt 3.0))) (/ 1.0 (cbrt 3.0))))))))
6.0ms
(/ 1.0 (cbrt 3.0))
6.0ms
(/ 1.0 (cbrt 3.0))
6.0ms
(/ 1.0 (cbrt 3.0))

series146.0ms

Counts
4 → 6
Calls
4 calls:
145.0ms
(/ 1.0 (sqrt (+ (fma a 9.0 (* 9.0 (/ (- (/ 1.0 (cbrt 3.0))) (* (cbrt 3.0) (cbrt 3.0))))) (* 9.0 (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (+ (- (/ 1.0 (cbrt 3.0))) (/ 1.0 (cbrt 3.0))))))))
0.0ms
(/ 1.0 (cbrt 3.0))
0.0ms
(/ 1.0 (cbrt 3.0))
0.0ms
(/ 1.0 (cbrt 3.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03662433
112682268
250012253

prune788.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
794×times-frac
602×add-sqr-sqrt
446×sqrt-prod
438×*-un-lft-identity
346×add-cube-cbrt
210×associate-*l*
92×difference-of-squares
46×distribute-lft-out--
22×associate-/l*
21×div-inv
20×add-exp-log add-cbrt-cube
9×associate-/r*
8×pow1 unswap-sqr
6×cbrt-undiv div-exp associate-*r* add-log-exp
5×flip3-- flip--
4×expm1-log1p-u frac-times flip3-+ sqrt-div prod-exp associate-/r/ cbrt-unprod flip-+ log1p-expm1-u
3×fma-def associate-*l/
2×associate-*r/ pow-prod-down *-commutative
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in clear-num sum-log associate-/l/
Counts
4 → 529
Calls
4 calls:
11.0ms
(+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand))
77.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
113.0ms
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
33.0ms
(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series702.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand))
152.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
213.0ms
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
176.0ms
(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
541 → 541
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
016776837
150026547

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes91.0ms

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)

IterNodesCost
03929
14329
24629
34629

end0.0ms

sample2.0s

Algorithm
intervals
Results
955.0ms27957×body80nan
296.0ms9095×body80valid