Details

Time bar (total: 5.5s)

sample23.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms223×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
15.1b
(/ (- (* 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))))
9.0ms
(/ (- (* a a) (* b b)) (* a a))

series72.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
54.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify138.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
0197340
1816296
24110295
35001292

prune110.0ms

Filtered
45 candidates to 34 candidates (75.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
51×*-un-lft-identity
46×times-frac
31×add-cube-cbrt
19×associate-*r*
17×add-exp-log add-cbrt-cube
16×associate-*l*
7×distribute-lft-out-- difference-of-squares
6×pow1
5×cbrt-undiv div-exp associate-/l*
4×prod-exp cbrt-unprod unswap-sqr
3×associate-/r* sqrt-prod div-inv distribute-lft-out add-log-exp
2×associate-/l/
1×frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip--
Counts
3 → 110
Calls
3 calls:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
31.0ms
(* (/ (+ a b) a) (/ (- a b) a))
8.0ms
(/ (- a b) a)

series112.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
65.0ms
(* (/ (+ a b) a) (/ (- a b) a))
31.0ms
(/ (- a b) a)

simplify59.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0452789
12284718
25002715

prune252.0ms

Filtered
119 candidates to 81 candidates (68.1%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (fabs (* (/ (+ a b) a) (/ 1 (/ a (- a b))))))
0.0b
(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
0.0b
(/ 1 (/ a (- a b)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
195×add-sqr-sqrt
171×*-un-lft-identity
119×add-cube-cbrt
68×associate-*r*
59×add-exp-log
29×add-cbrt-cube
28×div-exp
21×associate-/r* distribute-lft-out-- difference-of-squares
16×associate-*l* associate-/r/
14×prod-exp
12×cbrt-undiv
10×div-inv unswap-sqr
7×pow1 flip3-- flip--
6×rec-exp 1-exp cbrt-unprod
3×sqrt-prod distribute-lft-out associate-/l* add-log-exp
1×frac-times rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative inv-pow
Counts
3 → 248
Calls
3 calls:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ 1 (/ a (- a b))))))
58.0ms
(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
10.0ms
(/ 1 (/ a (- a b)))

series112.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ 1 (/ a (- a b))))))
64.0ms
(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
32.0ms
(/ 1 (/ a (- a b)))

simplify47.0ms

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010042152
150011883

prune531.0ms

Filtered
257 candidates to 159 candidates (61.9%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (/ (+ a b) a) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt a) (+ (sqrt a) (sqrt b))))) (/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b)))))
0.1b
(/ (sqrt a) (- (sqrt a) (sqrt b)))
0.1b
(/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b))))
0.1b
(/ (sqrt a) (+ (sqrt a) (sqrt b)))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
1506×times-frac
1298×add-sqr-sqrt
986×*-un-lft-identity
923×sqrt-prod
618×add-cube-cbrt
365×associate-*r*
363×cbrt-prod
340×difference-of-squares
205×add-exp-log
170×distribute-lft-out--
157×add-cbrt-cube
89×cbrt-undiv div-exp
75×prod-exp cbrt-unprod
74×associate-/r*
32×associate-/r/
18×associate-/l*
17×div-inv
14×flip3-- flip-- distribute-lft-out
9×pow1
5×frac-times associate-*l/
4×add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
1×flip3-+ associate-*l* *-commutative flip-+
Counts
4 → 1028
Calls
4 calls:
185.0ms
(* (* (/ (+ a b) a) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt a) (+ (sqrt a) (sqrt b))))) (/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b)))))
16.0ms
(/ (sqrt a) (- (sqrt a) (sqrt b)))
27.0ms
(/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b))))
12.0ms
(/ (sqrt a) (+ (sqrt a) (sqrt b)))

series669.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(* (* (/ (+ a b) a) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt a) (+ (sqrt a) (sqrt b))))) (/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b)))))
118.0ms
(/ (sqrt a) (- (sqrt a) (sqrt b)))
119.0ms
(/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b))))
104.0ms
(/ (sqrt a) (+ (sqrt a) (sqrt b)))

simplify203.0ms

Algorithm
egg-herbie
Counts
1040 → 1040
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0263020045
1500118819

prune1.9s

Filtered
1040 candidates to 365 candidates (35.1%)
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
0158
1158

end0.0ms

sample611.0ms

Algorithm
intervals
Results
190.0ms8000×body80valid
99.0ms8000×pre80true
93.0ms8030×pre80false