Details

Time bar (total: 4.3s)

sample12.0ms

Algorithm
intervals
Results
4.0ms236×body80valid
1.0ms9×body1280valid
0.0ms3×body640valid
0.0ms5×body320valid
0.0ms3×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0123
1193
2293
3413
4513
5793
61343
71693
81853
92133
102263
112263

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ x (/ (- x y) 2.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
3×*-un-lft-identity add-log-exp
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt associate-+r- flip3-+ div-sub sum-log add-cbrt-cube flip-+ distribute-lft-out
Counts
1 → 13
Calls
1 calls:
16.0ms
(+ x (/ (- x y) 2.0))

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(+ x (/ (- x y) 2.0))

simplify76.0ms

Algorithm
egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
09181
124274
270474
3341274
4500174

prune34.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ x (/ (- x y) 2.0)))
0.5b
(cbrt (+ x (/ (- x y) 2.0)))
0.5b
(cbrt (+ x (/ (- x y) 2.0)))
0.5b
(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
12.0ms
(cbrt (+ x (/ (- x y) 2.0)))
14.0ms
(cbrt (+ x (/ (- x y) 2.0)))
13.0ms
(cbrt (+ x (/ (- x y) 2.0)))
105.0ms
(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
426.0ms
(cbrt (+ x (/ (- x y) 2.0)))
426.0ms
(cbrt (+ x (/ (- x y) 2.0)))
427.0ms
(cbrt (+ x (/ (- x y) 2.0)))
392.0ms
(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))

simplify65.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
02631109
17591044
22601956
35001940

prune238.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- x (/ (- x y) 2.0))
0.0b
(* (/ (- x y) 2.0) (/ (- x y) 2.0))
12.5b
(- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0)))
29.7b
(/ (- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0))) (- x (/ (- x y) 2.0)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
122×add-sqr-sqrt
110×*-un-lft-identity
106×times-frac
56×add-cube-cbrt
32×difference-of-squares
25×swap-sqr
24×distribute-lft-out--
19×associate-*r* associate-*l*
18×add-exp-log add-cbrt-cube
11×pow1
8×add-log-exp
6×associate-/r*
5×cbrt-undiv div-exp div-inv
4×flip3-- prod-exp flip-- cbrt-unprod associate-/l* unswap-sqr
2×sub-neg diff-log div-sub associate-/r/ associate-/l/
1×pow2 frac-times frac-2neg pow-plus associate-*r/ pow-prod-down associate-*l/ clear-num pow-sqr *-commutative pow-prod-up associate--r-
Counts
4 → 171
Calls
4 calls:
12.0ms
(- x (/ (- x y) 2.0))
32.0ms
(* (/ (- x y) 2.0) (/ (- x y) 2.0))
3.0ms
(- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0)))
36.0ms
(/ (- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0))) (- x (/ (- x y) 2.0)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- x (/ (- x y) 2.0))
24.0ms
(* (/ (- x y) 2.0) (/ (- x y) 2.0))
35.0ms
(- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0)))
104.0ms
(/ (- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0))) (- x (/ (- x y) 2.0)))

simplify119.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
07671986
140211797
250011766

prune373.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ (- x y) 2.0))
0.0b
(sqrt (+ x (/ (- x y) 2.0)))
0.0b
(sqrt (+ x (/ (- x y) 2.0)))
0.2b
(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity sqrt-prod
28×add-sqr-sqrt
21×pow1
16×sqrt-div
14×add-cube-cbrt
11×swap-sqr
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 associate-+r- pow-plus sqrt-unprod div-sub prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 107
Calls
4 calls:
13.0ms
(+ x (/ (- x y) 2.0))
25.0ms
(sqrt (+ x (/ (- x y) 2.0)))
24.0ms
(sqrt (+ x (/ (- x y) 2.0)))
109.0ms
(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

series256.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ x (/ (- x y) 2.0))
91.0ms
(sqrt (+ x (/ (- x y) 2.0)))
90.0ms
(sqrt (+ x (/ (- x y) 2.0)))
39.0ms
(* (sqrt (+ x (/ (- x y) 2.0))) (sqrt (+ x (/ (- x y) 2.0))))

simplify196.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0235813
1879731
24785705
35001705

prune174.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.0b 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
073
173

end0.0ms

sample288.0ms

Algorithm
intervals
Results
132.0ms7414×body80valid
16.0ms220×body1280valid
8.0ms148×body640valid
6.0ms74×body2560valid
4.0ms96×body320valid
2.0ms57×body160valid