Details

Time bar (total: 3.5s)

sample24.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms300×pre80false
3.0ms256×pre80true

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1477
21067
32657
414957
550017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* a a) (* b b))
0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
13.5b
(/ (- (* a a) (* b b)) (* a a))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
8×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
5×add-log-exp
4×pow1 times-frac associate-/l*
3×sqrt-prod difference-of-squares
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 52
Calls
3 calls:
3.0ms
(- (* a a) (* b b))
1.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
7.0ms
(/ (- (* a a) (* b b)) (* a a))

series105.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(- (* a a) (* b b))
18.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
55.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify167.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (157.0ms)

IterNodesCost
0228417
1970368
24781367
35001366

prune142.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ a b) a)
0.0b
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b
(* (/ (+ a b) a) (/ (- a b) a))
0.1b
(/ (- a b) a)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
68×add-sqr-sqrt
58×times-frac
41×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*r*
16×associate-*l*
9×associate-/l*
7×pow1 distribute-lft-out distribute-lft-out-- difference-of-squares
6×cbrt-undiv div-exp associate-/r*
4×prod-exp cbrt-unprod div-inv associate-/l/ add-log-exp unswap-sqr
3×sqrt-prod
2×frac-2neg clear-num
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 143
Calls
4 calls:
5.0ms
(/ (+ a b) a)
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
19.0ms
(* (/ (+ a b) a) (/ (- a b) a))
6.0ms
(/ (- a b) a)

series134.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ (+ a b) a)
16.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
65.0ms
(* (/ (+ a b) a) (/ (- a b) a))
31.0ms
(/ (- a b) a)

simplify63.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0493952
12505870
25001867

prune335.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (+ a b) (/ (- a b) a)) a)
0.0b
(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
0.0b
(* (+ a b) (/ (- a b) a))
0.1b
(/ (- a b) a)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
43×*-un-lft-identity
34×times-frac
27×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*r*
7×pow1 associate-/l/ distribute-lft-out-- difference-of-squares
6×cbrt-undiv div-exp associate-/r* associate-/l*
4×frac-times flip3-+ associate-*l* associate-*l/ prod-exp cbrt-unprod flip-+ add-log-exp
3×sqrt-prod div-inv
2×frac-2neg associate-*r/ clear-num unswap-sqr
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 div-sub pow-prod-down *-commutative flip-- distribute-lft-out
Counts
4 → 122
Calls
4 calls:
10.0ms
(/ (* (+ a b) (/ (- a b) a)) a)
1.0ms
(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
15.0ms
(* (+ a b) (/ (- a b) a))
6.0ms
(/ (- a b) a)

series172.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (* (+ a b) (/ (- a b) a)) a)
15.0ms
(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
62.0ms
(* (+ a b) (/ (- a b) a))
30.0ms
(/ (- a b) a)

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0440816
12436731
25002729

prune466.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a)))
0.0b
(* (* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a))) (* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a))))
0.1b
(/ (- a b) a)
0.1b
(/ (- a b) a)

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt
104×times-frac
95×*-un-lft-identity
86×sqrt-prod
61×add-cube-cbrt
49×add-exp-log add-cbrt-cube
47×associate-*l*
45×pow1
23×associate-*r* prod-exp cbrt-unprod
18×frac-times sqrt-div pow-prod-down
15×unswap-sqr
12×associate-*r/ associate-*l/
11×distribute-lft-out-- difference-of-squares
10×associate-/l*
9×cbrt-undiv div-exp
6×sqrt-unprod associate-/r* distribute-lft-out
5×sqrt-undiv
4×pow-sqr pow-prod-up div-inv associate-/l/ add-log-exp
2×flip3-- frac-2neg pow-plus div-sub clear-num *-commutative flip--
1×pow2 swap-sqr rem-square-sqrt
Counts
4 → 237
Calls
4 calls:
30.0ms
(* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a)))
29.0ms
(* (* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a))) (* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a))))
6.0ms
(/ (- a b) a)
6.0ms
(/ (- a b) a)

series272.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a)))
96.0ms
(* (* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a))) (* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a))))
35.0ms
(/ (- a b) a)
31.0ms
(/ (- a b) a)

simplify81.0ms

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06352434
128341980
250011853

prune623.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0117
1117

end0.0ms

sample594.0ms

Algorithm
intervals
Results
190.0ms8000×body80valid
93.0ms7922×pre80false
92.0ms8000×pre80true