Details

Time bar (total: 4.5s)

sample24.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms263×pre80false
3.0ms256×pre80true

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0197
1487
21107
32847
415807
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

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))))
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×expm1-log1p-u sqrt-prod log1p-expm1-u difference-of-squares
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 60
Calls
3 calls:
3.0ms
(- (* a a) (* b b))
1.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
9.0ms
(/ (- (* a a) (* b b)) (* a a))

series105.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(- (* a a) (* b b))
17.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
53.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify31.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0241458
11037405
25001401

prune178.0ms

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))

rewrite52.0ms

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×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u 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 → 151
Calls
4 calls:
8.0ms
(/ (- a b) a)
7.0ms
(/ (+ a b) a)
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
31.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series131.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (- a b) a)
21.0ms
(/ (+ a b) a)
16.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
64.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify270.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0505990
12546909
25001905

prune381.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
126×add-sqr-sqrt
116×*-un-lft-identity
101×sqrt-prod
92×associate-*l*
78×add-cube-cbrt
59×add-exp-log add-cbrt-cube
22×prod-exp cbrt-unprod
20×associate-*r*
18×cbrt-undiv div-exp
12×pow1 distribute-lft-out
10×unswap-sqr
7×distribute-lft-out-- difference-of-squares
6×frac-times associate-*r/
5×associate-/l*
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u div-inv add-log-exp
3×associate-/r*
2×*-commutative associate-/l/
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub clear-num flip--
Counts
4 → 238
Calls
4 calls:
8.0ms
(/ (- a b) a)
1.0ms
(sqrt (fabs (* (/ (sqrt (+ a b)) (sqrt a)) (* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a)))))
59.0ms
(* (/ (sqrt (+ a b)) (sqrt a)) (* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a)))
45.0ms
(* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a))

series248.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (- a b) a)
19.0ms
(sqrt (fabs (* (/ (sqrt (+ a b)) (sqrt a)) (* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a)))))
97.0ms
(* (/ (sqrt (+ a b)) (sqrt a)) (* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a)))
99.0ms
(* (/ (sqrt (+ a b)) (sqrt a)) (/ (- a b) a))

simplify125.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
08202767
148132260
250012249

prune644.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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))
0.1b
(/ (- (sqrt a) (sqrt b)) (sqrt a))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
196×add-sqr-sqrt
185×sqrt-prod
144×*-un-lft-identity
108×times-frac
84×add-cube-cbrt
58×associate-*r*
56×difference-of-squares
47×add-exp-log add-cbrt-cube
36×prod-diff
28×distribute-lft-out--
18×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
9×pow1 associate-/l*
8×add-log-exp
6×fma-def fma-neg associate-/r*
5×frac-times associate-*l/
4×expm1-log1p-u log1p-expm1-u
3×associate-*r/ pow-prod-down
2×flip3-- flip-- div-inv associate-/l/ distribute-lft-out
1×+-commutative sub-neg frac-2neg flip3-+ diff-log div-sub associate-*l* clear-num sum-log *-commutative flip-+
Counts
4 → 267
Calls
4 calls:
6.0ms
(+ (sqrt a) (sqrt b))
76.0ms
(* (* (/ (+ a b) a) (/ (+ (sqrt a) (sqrt b)) (sqrt a))) (/ (- (sqrt a) (sqrt b)) (sqrt a)))
8.0ms
(- (sqrt a) (sqrt b))
22.0ms
(/ (- (sqrt a) (sqrt b)) (sqrt a))

series542.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(+ (sqrt a) (sqrt b))
320.0ms
(* (* (/ (+ a b) a) (/ (+ (sqrt a) (sqrt b)) (sqrt a))) (/ (- (sqrt a) (sqrt b)) (sqrt a)))
55.0ms
(- (sqrt a) (sqrt b))
113.0ms
(/ (- (sqrt a) (sqrt b)) (sqrt a))

simplify57.0ms

Algorithm
egg-herbie
Counts
279 → 279
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09323699
150013086

prune681.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

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

sample626.0ms

Algorithm
intervals
Results
195.0ms8000×body80valid
99.0ms8000×pre80true
99.0ms8133×pre80false