Details

Time bar (total: 3.9s)

sample24.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms261×pre80false
3.0ms256×pre80true

simplify49.0ms

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: 15.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
0.0b
(- (* a a) (* b b))
14.9b
(/ (- (* a a) (* b b)) (* a a))

rewrite12.0ms

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

series99.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
33.0ms
(- (* a a) (* b b))
49.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify164.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (158.0ms)

IterNodesCost
0228417
1970368
24781367
35001366

prune137.0ms

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
(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))

rewrite47.0ms

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))))
7.0ms
(/ (+ a b) a)
7.0ms
(/ (- a b) a)
27.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series129.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms
(/ (+ a b) a)
32.0ms
(/ (- a b) a)
60.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0493951
12505870
25001867

prune330.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
52×*-un-lft-identity
46×times-frac
32×add-cube-cbrt
19×associate-*r*
18×add-exp-log add-cbrt-cube
16×associate-*l*
7×pow1 distribute-lft-out-- add-log-exp difference-of-squares
5×cbrt-undiv div-exp associate-/l*
4×prod-exp cbrt-unprod unswap-sqr
3×log-prod associate-/r* log-pow div-inv distribute-lft-out
2×exp-prod exp-to-pow associate-/l/
1×frac-times flip3-- frac-2neg div-sub associate-*r/ rem-log-exp pow-prod-down associate-*l/ clear-num *-commutative flip-- rem-exp-log
Counts
4 → 121
Calls
4 calls:
1.0ms
(exp (* (/ (+ a b) a) (/ (- a b) a)))
2.0ms
(log (exp (* (/ (+ a b) a) (/ (- a b) a))))
7.0ms
(/ (- a b) a)
30.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series206.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(exp (* (/ (+ a b) a) (/ (- a b) a)))
57.0ms
(log (exp (* (/ (+ a b) a) (/ (- a b) a))))
32.0ms
(/ (- a b) a)
58.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify59.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0458859
12310763
25001761

prune340.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
212×add-sqr-sqrt
170×sqrt-prod
167×*-un-lft-identity
157×times-frac
92×associate-*r*
81×add-cube-cbrt
59×add-exp-log add-cbrt-cube
56×difference-of-squares
28×distribute-lft-out--
22×prod-exp cbrt-unprod
18×cbrt-undiv div-exp
17×associate-*l*
15×distribute-lft-out
11×pow1
9×associate-/l*
6×frac-times associate-*l/ associate-/r* add-log-exp unswap-sqr
4×associate-*r/ pow-prod-down div-inv
2×flip3-- *-commutative flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub clear-num
Counts
4 → 274
Calls
4 calls:
44.0ms
(* (/ (+ a b) a) (/ (+ (sqrt a) (sqrt b)) (sqrt a)))
6.0ms
(- (sqrt a) (sqrt b))
76.0ms
(* (* (/ (+ a b) a) (/ (+ (sqrt a) (sqrt b)) (sqrt a))) (/ (- (sqrt a) (sqrt b)) (sqrt a)))
17.0ms
(/ (- (sqrt a) (sqrt b)) (sqrt a))

series632.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(* (/ (+ a b) a) (/ (+ (sqrt a) (sqrt b)) (sqrt a)))
49.0ms
(- (sqrt a) (sqrt b))
305.0ms
(* (* (/ (+ a b) a) (/ (+ (sqrt a) (sqrt b)) (sqrt a))) (/ (- (sqrt a) (sqrt b)) (sqrt a)))
111.0ms
(/ (- (sqrt a) (sqrt b)) (sqrt a))

simplify57.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010513672
150023225

prune631.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

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
0139
1139

end0.0ms

sample617.0ms

Algorithm
intervals
Results
189.0ms8000×body80valid
104.0ms8127×pre80false
95.0ms8000×pre80true