Details

Time bar (total: 3.6s)

sample23.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms256×pre80true
3.0ms250×pre80false

simplify51.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.6b

Counts
2 → 1

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))))
12.2b
(/ (- (* 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×sqrt-prod difference-of-squares
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 52
Calls
3 calls:
3.0ms
(- (* a a) (* b b))
1.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
7.0ms
(/ (- (* a a) (* b b)) (* a a))

series108.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(- (* a a) (* b b))
18.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
58.0ms
(/ (- (* a a) (* b b)) (* a a))

simplify162.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (156.0ms)

IterNodesCost
0228417
1970368
24781367
35001366

prune124.0ms

Filtered
61 candidates to 45 candidates (73.8%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New59261
Fresh000
Picked101
Done000
Total60262

Merged error: 0.0b

Counts
62 → 2

localize9.0ms

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

rewrite38.0ms

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×prod-exp cbrt-unprod 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 → 143
Calls
4 calls:
1.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
5.0ms
(/ (+ a b) a)
6.0ms
(/ (- a b) a)
20.0ms
(* (/ (+ a b) a) (/ (- a b) a))

series134.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
22.0ms
(/ (+ a b) a)
31.0ms
(/ (- a b) a)
66.0ms
(* (/ (+ a b) a) (/ (- a b) a))

simplify66.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0493952
12505870
25001867

prune281.0ms

Filtered
155 candidates to 106 candidates (68.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1541155
Fresh011
Picked011
Done000
Total1543157

Merged error: 0b

Counts
157 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
138×add-sqr-sqrt
102×*-un-lft-identity
96×times-frac
94×sqrt-prod
62×add-cube-cbrt
44×associate-*r*
38×associate-*l*
18×unswap-sqr
14×distribute-lft-out-- difference-of-squares
12×pow1 add-exp-log add-cbrt-cube
10×associate-/l*
8×sqrt-div
6×pow-prod-down associate-/r* div-inv distribute-lft-out
4×sqrt-pow1 pow1/2 associate-/l/ add-log-exp
2×cbrt-undiv frac-times flip3-- frac-2neg sqrt-unprod div-sub associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative flip-- cbrt-unprod
Counts
4 → 210
Calls
4 calls:
24.0ms
(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
20.0ms
(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
6.0ms
(/ (- a b) a)
6.0ms
(/ (- a b) a)

series460.0ms

Counts
4 → 12
Calls
4 calls:
291.0ms
(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
108.0ms
(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
30.0ms
(/ (- a b) a)
31.0ms
(/ (- a b) a)

simplify52.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03321694
112461636
250021622

prune573.0ms

Filtered
222 candidates to 158 candidates (71.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2220222
Fresh011
Picked011
Done011
Total2223225

Merged error: 0b

Counts
225 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (- (* a a) (* b b))) a)
0.0b
(* (/ (sqrt (- (* a a) (* b b))) a) (/ (sqrt (- (* a a) (* b b))) a))
12.5b
(sqrt (- (* a a) (* b b)))
12.5b
(sqrt (- (* a a) (* b b)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
129×times-frac
126×add-sqr-sqrt
84×sqrt-prod
82×add-cube-cbrt *-un-lft-identity
31×swap-sqr
25×associate-*r* associate-*l*
18×add-exp-log add-cbrt-cube difference-of-squares
13×pow1
9×unswap-sqr
7×associate-/l*
6×sqrt-div
5×cbrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod add-log-exp
3×flip3-- associate-/r* flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×pow2 frac-times frac-2neg pow-plus associate-*r/ pow-prod-down associate-*l/ clear-num pow-sqr *-commutative pow-prod-up
Counts
4 → 191
Calls
4 calls:
6.0ms
(/ (sqrt (- (* a a) (* b b))) a)
24.0ms
(* (/ (sqrt (- (* a a) (* b b))) a) (/ (sqrt (- (* a a) (* b b))) a))
4.0ms
(sqrt (- (* a a) (* b b)))
4.0ms
(sqrt (- (* a a) (* b b)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (sqrt (- (* a a) (* b b))) a)
50.0ms
(* (/ (sqrt (- (* a a) (* b b))) a) (/ (sqrt (- (* a a) (* b b))) a))
49.0ms
(sqrt (- (* a a) (* b b)))
48.0ms
(sqrt (- (* a a) (* b b)))

simplify84.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06182481
130242161
250011973

prune400.0ms

Filtered
203 candidates to 133 candidates (65.5%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2030203
Fresh000
Picked011
Done022
Total2033206

Merged error: 0b

Counts
206 → 3

regimes47.0ms

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

sample601.0ms

Algorithm
intervals
Results
193.0ms8000×body80valid
95.0ms8000×pre80true
91.0ms7937×pre80false