Details

Time bar (total: 6.6s)

sample52.0ms

Algorithm
intervals
Results
12.0ms189×body80valid
7.0ms21×body1280valid
6.0ms121×body80nan
4.0ms16×body640valid
3.0ms17×body320valid
3.0ms10×body1280nan
2.0ms8×body640nan
1.0ms13×body160valid
1.0ms9×body320nan
0.0ms3×body160nan

simplify24.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0196
1296
2416
3606
4786
5946
61096
71396
82146
92796
102796

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b
(/ (- x y) (- 1.0 y))
3.1b
(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.5b
(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
51×*-un-lft-identity
28×times-frac
19×difference-of-squares
18×add-cube-cbrt
17×distribute-lft-out--
12×log-prod
7×add-exp-log add-log-exp
6×pow1 flip3-- add-cbrt-cube flip-- associate--r+
5×associate-/r* associate-/l*
4×log-div
3×associate--r-
2×sub-neg diff-log div-sub associate-/r/ log-pow associate-/l/
1×cbrt-undiv frac-2neg div-exp rem-log-exp clear-num div-inv
Counts
4 → 108
Calls
4 calls:
25.0ms
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
11.0ms
(/ (- x y) (- 1.0 y))
20.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))
19.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
42.0ms
(/ (- x y) (- 1.0 y))
88.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))
53.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))

simplify49.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0488942
11388894
25001876

prune317.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (- 1.0 y))
0.2b
(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
3.1b
(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
11.0b
(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
32×add-sqr-sqrt
30×*-un-lft-identity
14×add-cube-cbrt cbrt-div
12×pow1
10×swap-sqr
9×flip3-- flip--
8×associate-*r* associate-*l*
7×add-exp-log pow1/3 distribute-lft-out--
6×add-log-exp
5×difference-of-squares
4×frac-times add-cbrt-cube unswap-sqr
3×log-prod
2×log-div associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus diff-log rem-log-exp prod-exp log-pow *-commutative cbrt-unprod
Counts
4 → 97
Calls
4 calls:
2.0ms
(cbrt (- 1.0 y))
22.0ms
(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
2.0ms
(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
2.0ms
(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(cbrt (- 1.0 y))
110.0ms
(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
95.0ms
(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
60.0ms
(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04711207
116151111
250011046

prune333.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (/ (- x y) (- 1.0 y)) 3)
3.1b
(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
3.5b
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
12.8b
(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

rewrite513.0ms

Algorithm
rewrite-expression-head
Rules
510×add-sqr-sqrt
312×times-frac
222×*-un-lft-identity
212×difference-of-squares
175×unpow-prod-down cube-prod
105×log-prod
102×add-cube-cbrt
81×sqr-pow
60×distribute-lft-out--
33×associate-/l*
12×add-exp-log
9×add-cbrt-cube
8×difference-cubes associate-/r/
6×pow1 add-log-exp
4×flip3-- flip-- div-inv
3×pow-unpow div-exp associate-/r*
2×cbrt-undiv flip3-+ rem-log-exp pow-exp flip-+ associate-/l/ rem-cube-cbrt
1×cube-div cube-mult pow-to-exp sub-neg log-div pow-pow frac-2neg diff-log unpow3 div-sub clear-num log-pow
Counts
4 → 392
Calls
4 calls:
13.0ms
(pow (/ (- x y) (- 1.0 y)) 3)
112.0ms
(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
74.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
286.0ms
(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

series922.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(pow (/ (- x y) (- 1.0 y)) 3)
374.0ms
(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
195.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
284.0ms
(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

simplify125.0ms

Algorithm
egg-herbie
Counts
404 → 404
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0135910607
1500210369

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (/ x y) (* 1.0 (/ x (pow y 2)))) (* 1.0 (/ 1 y)))
1.9b
(log (- (+ (/ x y) (* 1.0 (/ x (pow y 2)))) (* 1.0 (/ 1 y))))
4.5b
(+ (/ x y) (* 1.0 (/ x (pow y 2))))
12.0b
(/ x (pow y 2))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down frac-sub
11×associate-*r/ add-log-exp
10×add-exp-log
8×log-div associate-/r*
6×un-div-inv add-cbrt-cube
5×pow1 flip3-+ frac-add flip-+
4×unpow2 sqr-pow
3×log-prod div-exp associate-/l*
2×flip3-- diff-log sum-log flip--
1×cbrt-undiv +-commutative pow-to-exp sub-neg frac-2neg rem-log-exp pow-exp associate--l+ clear-num log-pow div-inv
Counts
4 → 101
Calls
4 calls:
56.0ms
(- (+ (/ x y) (* 1.0 (/ x (pow y 2)))) (* 1.0 (/ 1 y)))
24.0ms
(log (- (+ (/ x y) (* 1.0 (/ x (pow y 2)))) (* 1.0 (/ 1 y))))
8.0ms
(+ (/ x y) (* 1.0 (/ x (pow y 2))))
4.0ms
(/ x (pow y 2))

series185.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (+ (/ x y) (* 1.0 (/ x (pow y 2)))) (* 1.0 (/ 1 y)))
71.0ms
(log (- (+ (/ x y) (* 1.0 (/ x (pow y 2)))) (* 1.0 (/ 1 y))))
54.0ms
(+ (/ x y) (* 1.0 (/ x (pow y 2))))
25.0ms
(/ x (pow y 2))

simplify63.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04621166
118471050
250011036

prune300.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 17.0b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03527
13527

end0.0ms

sample1.6s

Algorithm
intervals
Results
374.0ms5666×body80valid
265.0ms810×body1280valid
203.0ms3633×body80nan
201.0ms834×body640valid
106.0ms360×body1280nan
81.0ms363×body640nan
79.0ms450×body320valid
37.0ms213×body320nan
28.0ms240×body160valid
10.0ms93×body160nan