Details

Time bar (total: 3.5s)

sample25.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
4.0ms300×pre80false
3.0ms256×pre80true

simplify55.0ms

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: 13.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* a a) (* b b))
0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
13.5b
(/ (- (* a a) (* b b)) (* a a))

rewrite14.0ms

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))

series98.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(- (* a a) (* b b))
17.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
52.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify31.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0241458
11037405
25001401

prune169.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ a b) a)
0.0b
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b
(* (/ (+ a b) a) (/ (- a b) a))
0.1b
(/ (- 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×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)
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
29.0ms
(* (/ (+ a b) a) (/ (- a b) a))
9.0ms
(/ (- a b) a)

series131.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (+ a b) a)
20.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
56.0ms
(* (/ (+ a b) a) (/ (- a b) a))
33.0ms
(/ (- a b) a)

simplify64.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0505990
12546909
25001905

prune363.0ms

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
(/ a (- a b))
0.0b
(sqrt (fabs (* (/ (+ a b) a) (/ 1 (/ a (- a b))))))
0.0b
(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
0.1b
(/ 1 (/ a (- a b)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
275×times-frac
214×add-sqr-sqrt
190×*-un-lft-identity
130×add-cube-cbrt
68×associate-*r*
62×add-exp-log
32×add-cbrt-cube
29×div-exp
26×associate-/r*
25×distribute-lft-out-- difference-of-squares
18×associate-/r/
16×associate-*l*
14×prod-exp
13×cbrt-undiv
11×div-inv
10×unswap-sqr
8×pow1 flip3-- flip--
6×rec-exp 1-exp cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod distribute-lft-out
2×frac-2neg clear-num
1×frac-times rem-sqrt-square pow-flip sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ un-div-inv *-commutative inv-pow
Counts
4 → 293
Calls
4 calls:
5.0ms
(/ a (- a b))
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ 1 (/ a (- a b))))))
59.0ms
(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
10.0ms
(/ 1 (/ a (- a b)))

series159.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ a (- a b))
16.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ 1 (/ a (- a b))))))
65.0ms
(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
31.0ms
(/ 1 (/ a (- a b)))

simplify50.0ms

Algorithm
egg-herbie
Counts
305 → 305
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010322385
150012105

prune682.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fabs (* (/ (+ a b) a) (expm1 (log1p (/ 1 (/ a (- a b))))))))
0.0b
(* (/ (+ a b) a) (expm1 (log1p (/ 1 (/ a (- a b))))))
0.1b
(expm1 (log1p (/ 1 (/ a (- a b)))))
0.1b
(/ 1 (/ a (- a b)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
136×times-frac
102×add-sqr-sqrt *-un-lft-identity
72×add-cube-cbrt
21×associate-/r*
20×add-exp-log
16×associate-*l*
14×add-cbrt-cube
12×distribute-lft-out-- difference-of-squares
9×associate-/r/
8×pow1 div-exp
6×div-inv
4×cbrt-undiv expm1-log1p-u flip3-- flip-- log1p-expm1-u add-log-exp
3×associate-*r* sqrt-prod distribute-lft-out associate-/l*
2×rec-exp 1-exp prod-exp cbrt-unprod unswap-sqr
1×rem-sqrt-square expm1-log1p pow-flip frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num *-commutative inv-pow expm1-udef
Counts
4 → 173
Calls
4 calls:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (expm1 (log1p (/ 1 (/ a (- a b))))))))
15.0ms
(* (/ (+ a b) a) (expm1 (log1p (/ 1 (/ a (- a b))))))
0.0ms
(expm1 (log1p (/ 1 (/ a (- a b)))))
13.0ms
(/ 1 (/ a (- a b)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (fabs (* (/ (+ a b) a) (expm1 (log1p (/ 1 (/ a (- a b))))))))
164.0ms
(* (/ (+ a b) a) (expm1 (log1p (/ 1 (/ a (- a b))))))
101.0ms
(expm1 (log1p (/ 1 (/ a (- a b)))))
30.0ms
(/ 1 (/ a (- a b)))

simplify75.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06441505
128681295
250031162

prune391.0ms

Pruning

3 alts after pruning (1 fresh and 2 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
01710
11710

end0.0ms

sample602.0ms

Algorithm
intervals
Results
180.0ms8000×body80valid
95.0ms8000×pre80true
92.0ms7922×pre80false