Details

Time bar (total: 5.5s)

sample24.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms256×pre80true
3.0ms223×pre80false

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1487
21107
32847
415807
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

localize7.0ms

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))

rewrite11.0ms

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 expm1-log1p-u div-exp log1p-expm1-u 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 → 43
Calls
2 calls:
1.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
9.0ms
(/ (- (* a a) (* b b)) (* a a))

series70.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
53.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify143.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (138.0ms)

IterNodesCost
0205367
1860319
24279318
35001316

prune119.0ms

Filtered
49 candidates to 38 candidates (77.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)

rewrite41.0ms

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×expm1-log1p-u associate-/r* sqrt-prod log1p-expm1-u 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 → 116
Calls
3 calls:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
28.0ms
(* (/ (+ a b) a) (/ (- a b) a))
8.0ms
(/ (- a b) a)

series109.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
58.0ms
(* (/ (+ a b) a) (/ (- a b) a))
35.0ms
(/ (- a b) a)

simplify64.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0460822
12313751
25001748

prune268.0ms

Filtered
125 candidates to 87 candidates (69.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

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)))

rewrite81.0ms

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×expm1-log1p-u sqrt-prod log1p-expm1-u 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 → 254
Calls
3 calls:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ 1 (/ a (- a b))))))
52.0ms
(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
12.0ms
(/ 1 (/ a (- a b)))

series109.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ 1 (/ a (- a b))))))
63.0ms
(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
30.0ms
(/ 1 (/ a (- a b)))

simplify43.0ms

Algorithm
egg-herbie
Counts
263 → 263
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010132192
150011921

prune549.0ms

Filtered
263 candidates to 165 candidates (62.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

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)))

rewrite334.0ms

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×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
1×flip3-+ associate-*l* *-commutative flip-+
Counts
4 → 1036
Calls
4 calls:
177.0ms
(* (* (/ (+ a b) a) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt a) (+ (sqrt a) (sqrt b))))) (/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b)))))
15.0ms
(/ (sqrt a) (- (sqrt a) (sqrt b)))
25.0ms
(/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b))))
12.0ms
(/ (sqrt a) (+ (sqrt a) (sqrt b)))

series678.0ms

Counts
4 → 12
Calls
4 calls:
329.0ms
(* (* (/ (+ a b) a) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt a) (+ (sqrt a) (sqrt b))))) (/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b)))))
120.0ms
(/ (sqrt a) (- (sqrt a) (sqrt b)))
121.0ms
(/ (cbrt 1) (/ (sqrt a) (- (sqrt a) (sqrt b))))
107.0ms
(/ (sqrt a) (+ (sqrt a) (sqrt b)))

simplify201.0ms

Algorithm
egg-herbie
Counts
1048 → 1048
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0265120127
1500119038

prune2.0s

Filtered
1048 candidates to 373 candidates (35.6%)
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

sample592.0ms

Algorithm
intervals
Results
183.0ms8000×body80valid
91.0ms8000×pre80true
90.0ms8030×pre80false