Details

Time bar (total: 4.2s)

sample23.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms263×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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* a a) (* b b))
0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
11.7b
(/ (- (* 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:
2.0ms
(- (* a a) (* b b))
1.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
8.0ms
(/ (- (* a a) (* b b)) (* a a))

series101.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(- (* a a) (* b b))
16.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
49.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify165.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (159.0ms)

IterNodesCost
0228417
1970368
24781367
35001366

prune155.0ms

Pruning

3 alts after pruning (3 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
(/ (+ a b) a)
0.0b
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b
(* (/ (+ a b) a) (/ (- a b) a))

rewrite51.0ms

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:
7.0ms
(/ (- a b) a)
8.0ms
(/ (+ a b) a)
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
28.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series131.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (- a b) a)
26.0ms
(/ (+ a b) a)
16.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
59.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0493951
12505870
25001867

prune359.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
53×add-sqr-sqrt
43×times-frac
34×add-cube-cbrt
19×associate-*r*
18×add-exp-log add-cbrt-cube
16×associate-*l*
8×pow1
7×log-pow distribute-lft-out
6×exp-prod sqrt-prod
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod associate-/l* add-log-exp unswap-sqr
3×log-prod associate-/r* div-inv distribute-lft-out-- difference-of-squares
2×associate-/l/
1×frac-times rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ rem-log-exp pow-prod-down associate-*l/ clear-num *-commutative flip-+
Counts
4 → 123
Calls
4 calls:
2.0ms
(log (exp (sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))))
7.0ms
(/ (+ a b) a)
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
30.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series118.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(log (exp (sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))))
22.0ms
(/ (+ a b) a)
16.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
63.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify53.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0465954
12123866
25002864

prune358.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
240×sqrt-prod
219×add-sqr-sqrt
217×times-frac
192×*-un-lft-identity
134×add-cube-cbrt
104×associate-*r*
61×add-exp-log add-cbrt-cube
26×distribute-lft-out-- difference-of-squares
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
17×associate-*l*
16×associate-/l*
12×associate-/r*
11×pow1
10×unswap-sqr
6×frac-times associate-*l/
5×div-inv
4×sqrt-div associate-*r/ pow-prod-down associate-/l/ add-log-exp
3×distribute-lft-out
2×sqrt-undiv flip3-- frac-2neg clear-num *-commutative flip--
Counts
4 → 342
Calls
4 calls:
44.0ms
(* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a)))
64.0ms
(* (* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a))) (/ (sqrt (- a b)) (sqrt a)))
9.0ms
(/ (sqrt (- a b)) (sqrt a))
9.0ms
(/ (sqrt (- a b)) (sqrt a))

series527.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a)))
279.0ms
(* (* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a))) (/ (sqrt (- a b)) (sqrt a)))
81.0ms
(/ (sqrt (- a b)) (sqrt a))
83.0ms
(/ (sqrt (- a b)) (sqrt a))

simplify65.0ms

Algorithm
egg-herbie
Counts
354 → 354
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09903818
150013438

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes32.0ms

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
01716
11716

end0.0ms

sample602.0ms

Algorithm
intervals
Results
185.0ms8000×body80valid
97.0ms8133×pre80false
91.0ms8000×pre80true