Details

Time bar (total: 3.1s)

sample10.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063
163

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize7.0ms

Local error

Found 1 expressions with local error:

18.3b
(/ x (+ (* x x) 1.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
13.0ms
(/ x (+ (* x x) 1.0))

series54.0ms

Counts
1 → 3
Calls
1 calls:
54.0ms
(/ x (+ (* x x) 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0165210
1555195
21839192
35001192

prune58.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* x x) 1.0)))
0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
18.3b
(sqrt (+ (* x x) 1.0))
18.3b
(sqrt (+ (* x x) 1.0))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
30×sqrt-prod
12×associate-/r*
10×add-exp-log
8×pow1 sqrt-div add-cbrt-cube
6×associate-/l*
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×pow-flip sqrt-pow1 pow1/2 div-exp
2×cbrt-undiv rem-sqrt-square frac-2neg clear-num div-inv
1×rec-exp 1-exp inv-pow
Counts
4 → 118
Calls
4 calls:
17.0ms
(/ x (sqrt (+ (* x x) 1.0)))
17.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
9.0ms
(sqrt (+ (* x x) 1.0))
10.0ms
(sqrt (+ (* x x) 1.0))

series283.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ x (sqrt (+ (* x x) 1.0)))
75.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
47.0ms
(sqrt (+ (* x x) 1.0))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0388970
11519893
25002855

prune236.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
0.1b
(/ 1 (pow x 5))
0.3b
(/ 1 (pow x 3))
15.5b
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
196×add-sqr-sqrt
173×times-frac
112×*-un-lft-identity
63×difference-of-squares
56×unpow-prod-down
47×add-cube-cbrt
40×sqr-pow
26×cube-prod
22×add-exp-log
19×associate-/r*
12×div-exp
8×add-cbrt-cube add-log-exp
7×distribute-lft-out--
6×pow-to-exp rec-exp 1-exp pow-exp div-inv associate-/l*
4×pow1 cube-mult associate-+l+ unpow3
3×sub-neg associate-*r/ frac-add
2×cbrt-undiv distribute-rgt-in flip3-- pow-flip frac-2neg distribute-lft-in clear-num frac-sub flip-- inv-pow
1×+-commutative flip3-+ diff-log sum-log flip-+
Counts
4 → 227
Calls
4 calls:
83.0ms
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
9.0ms
(/ 1 (pow x 5))
9.0ms
(/ 1 (pow x 3))
79.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
48.0ms
(/ 1 (pow x 5))
32.0ms
(/ 1 (pow x 3))
96.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify87.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06871931
128791646
250011645

prune283.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* x x) 3)
0.7b
(/ x (+ (pow (* x x) 3) (pow 1.0 3)))
15.6b
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
28.2b
(* (/ x (+ (pow (* x x) 3) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
31×times-frac
30×add-sqr-sqrt
25×add-cube-cbrt
21×associate-*l*
14×pow1 add-exp-log add-cbrt-cube
9×add-log-exp
7×sum-cubes distribute-lft-out
6×pow-pow
5×flip3-+ associate-/r* flip-+
4×associate-/r/
3×pow-unpow associate-*r* prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv frac-times associate-+r+ associate-*r/ div-exp pow-prod-down pow-exp sum-log div-inv rem-cube-cbrt unswap-sqr
1×+-commutative pow2 distribute-rgt-in cube-mult pow-to-exp associate-+r- sub-neg unpow-prod-down frac-2neg distribute-lft-in pow-plus diff-log unpow3 cube-prod associate-*l/ clear-num pow-sqr *-commutative pow-prod-up sqr-pow
Counts
4 → 124
Calls
4 calls:
6.0ms
(pow (* x x) 3)
29.0ms
(/ x (+ (pow (* x x) 3) (pow 1.0 3)))
40.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
203.0ms
(* (/ x (+ (pow (* x x) 3) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

series421.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(pow (* x x) 3)
220.0ms
(/ x (+ (pow (* x x) 3) (pow 1.0 3)))
40.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
119.0ms
(* (/ x (+ (pow (* x x) 3) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

simplify109.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06631449
133861262
250021246

prune340.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes53.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch57.0ms

Steps
ItersRangePoint
9
41.96612619086958
53435221.69579046
414.462941397456
6
-1.312921234409977e+17
-17398359074955834.0
-2.532497333585514e+16

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04122
14122

end0.0ms

sample244.0ms

Algorithm
intervals
Results
135.0ms8000×body80valid