Details

Time bar (total: 3.4s)

sample33.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
5.0ms265×pre80false
5.0ms256×pre80true

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1487
21107
32847
415807
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* a a) (* b b))
0.0b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
12.7b
(/ (- (* 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))

series99.0ms

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

simplify31.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0241458
11037405
25001401

prune161.0ms

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

rewrite53.0ms

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:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
8.0ms
(/ (+ a b) a)
9.0ms
(/ (- a b) a)
31.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series132.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms
(/ (+ a b) a)
30.0ms
(/ (- a b) a)
62.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify66.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0505990
12546909
25001905

prune350.0ms

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
66×add-sqr-sqrt
58×times-frac
40×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*r*
16×associate-*l*
9×associate-/l*
7×distribute-lft-out distribute-lft-out-- difference-of-squares
6×pow1 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
2×frac-2neg clear-num
1×frac-times expm1-log1p flip3-- flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+ expm1-udef
Counts
4 → 147
Calls
4 calls:
7.0ms
(/ (+ a b) a)
0.0ms
(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
9.0ms
(/ (- a b) a)
31.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series242.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (+ a b) a)
124.0ms
(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
30.0ms
(/ (- a b) a)
62.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify66.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0511929
12554843
25002840

prune414.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ a b) a)
0.1b
(* (/ (+ a b) a) (cbrt (pow (- 1 (/ b a)) 3)))
0.1b
(pow (- 1 (/ b a)) 3)
0.1b
(cbrt (pow (- 1 (/ b a)) 3))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
69×*-un-lft-identity
52×cbrt-prod
41×times-frac
31×add-cube-cbrt
26×unpow-prod-down cube-prod
25×associate-*r*
24×difference-of-squares
16×associate-*l*
12×add-exp-log
10×add-cbrt-cube unswap-sqr
8×cube-div
7×pow1 distribute-lft-out
6×cbrt-div distribute-lft-out--
5×sqr-pow
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l* add-log-exp
3×cube-mult pow-unpow unpow3 associate-/r*
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/
1×pow-to-exp pow-pow frac-2neg flip3-+ pow1/3 pow-prod-down associate-*l/ pow-exp clear-num *-commutative rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 178
Calls
4 calls:
8.0ms
(/ (+ a b) a)
79.0ms
(* (/ (+ a b) a) (cbrt (pow (- 1 (/ b a)) 3)))
17.0ms
(pow (- 1 (/ b a)) 3)
15.0ms
(cbrt (pow (- 1 (/ b a)) 3))

series125.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (+ a b) a)
55.0ms
(* (/ (+ a b) a) (cbrt (pow (- 1 (/ b a)) 3)))
30.0ms
(pow (- 1 (/ b a)) 3)
16.0ms
(cbrt (pow (- 1 (/ b a)) 3))

simplify81.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05751208
129931131
250011112

prune388.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes26.0ms

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

sample896.0ms

Algorithm
intervals
Results
370.0ms8000×body80valid
150.0ms8000×pre80true
143.0ms7787×pre80false