Details

Time bar (total: 3.1s)

sample24.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms244×pre80false
3.0ms256×pre80true

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1477
21067
32657
414957
550017

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
14.1b
(/ (- (* a a) (* b b)) (* a a))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×add-exp-log add-cbrt-cube
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×times-frac associate-/l*
3×pow1 sqrt-prod
2×cbrt-undiv div-exp associate-/l/ add-log-exp difference-of-squares
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* flip-- cbrt-unprod div-inv
Counts
2 → 39
Calls
2 calls:
1.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
8.0ms
(/ (- (* a a) (* b b)) (* a a))

series83.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
65.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify140.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
0197340
1816296
24110295
35001292

prune123.0ms

Filtered
45 candidates to 34 candidates (75.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b
(/ (+ a b) a)
0.0b
(/ (- a b) a)
0.0b
(* (/ (+ a b) a) (/ (- 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:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
6.0ms
(/ (+ a b) a)
6.0ms
(/ (- a b) a)
17.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series127.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms
(/ (+ a b) a)
30.0ms
(/ (- a b) a)
60.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify66.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0493951
12505870
25001867

prune394.0ms

Filtered
155 candidates to 106 candidates (68.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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:
1.0ms
(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
13.0ms
(* (+ a b) (/ (- a b) a))
12.0ms
(/ (* (+ a b) (/ (- a b) a)) a)
6.0ms
(/ (- a b) a)

series167.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
58.0ms
(* (+ a b) (/ (- a b) a))
61.0ms
(/ (* (+ a b) (/ (- a b) a)) a)
31.0ms
(/ (- a b) a)

simplify66.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0440815
12436731
25001729

prune352.0ms

Filtered
134 candidates to 94 candidates (70.1%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (exp (/ (* (+ a b) (/ (- a b) a)) a)))
0.0b
(* (+ a b) (/ (- a b) a))
0.0b
(/ (* (+ a b) (/ (- a b) a)) a)
0.0b
(/ (- a b) a)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
45×*-un-lft-identity
37×times-frac
29×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*r*
8×log-pow
7×pow1 exp-prod 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-+ div-inv add-log-exp
3×log-prod
2×frac-2neg associate-*r/ clear-num unswap-sqr
1×flip3-- div-sub rem-log-exp pow-prod-down *-commutative flip-- distribute-lft-out
Counts
4 → 128
Calls
4 calls:
4.0ms
(log (exp (/ (* (+ a b) (/ (- a b) a)) a)))
13.0ms
(* (+ a b) (/ (- a b) a))
12.0ms
(/ (* (+ a b) (/ (- a b) a)) a)
7.0ms
(/ (- a b) a)

series211.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(log (exp (/ (* (+ a b) (/ (- a b) a)) a)))
56.0ms
(* (+ a b) (/ (- a b) a))
62.0ms
(/ (* (+ a b) (/ (- a b) a)) a)
31.0ms
(/ (- a b) a)

simplify65.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0447838
12417741
25001740

prune455.0ms

Filtered
140 candidates to 102 candidates (72.9%)
Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample641.0ms

Algorithm
intervals
Results
201.0ms8000×body80valid
105.0ms8096×pre80false
97.0ms8000×pre80true