Details

Time bar (total: 1.8s)

sample9.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073
173

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize6.0ms

Local error

Found 1 expressions with local error:

16.0b
(/ x (+ (* x x) 1.0))

rewrite7.0ms

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 expm1-log1p-u frac-2neg flip3-+ div-exp clear-num flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 31
Calls
1 calls:
6.0ms
(/ x (+ (* x x) 1.0))

series55.0ms

Counts
1 → 3
Calls
1 calls:
55.0ms
(/ x (+ (* x x) 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0171215
1589196
21979191
35002186

prune72.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
0.0b
(/ x (sqrt (+ (* x x) 1.0)))
15.9b
(sqrt (+ (* x x) 1.0))
15.9b
(sqrt (+ (* x x) 1.0))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
166×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
9×div-inv
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
1×associate-/l/
Counts
4 → 272
Calls
4 calls:
22.0ms
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
7.0ms
(/ x (sqrt (+ (* x x) 1.0)))
5.0ms
(sqrt (+ (* x x) 1.0))
5.0ms
(sqrt (+ (* x x) 1.0))

series269.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
119.0ms
(/ x (sqrt (+ (* x x) 1.0)))
47.0ms
(sqrt (+ (* x x) 1.0))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify82.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07933899
130513471
250023383

prune457.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 1 (pow x 5))
0.5b
(/ 1 (pow x 3))
20.1b
(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
57×times-frac
44×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
21×add-exp-log
19×associate-/r*
12×cube-prod div-exp
8×sqr-pow
7×add-cbrt-cube
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
4×cube-mult unpow3
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv pow-flip frac-2neg clear-num div-inv inv-pow
1×fma-udef
Counts
3 → 140
Calls
3 calls:
4.0ms
(/ 1 (pow x 5))
5.0ms
(/ 1 (pow x 3))
0.0ms
(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

series125.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(/ 1 (pow x 5))
31.0ms
(/ 1 (pow x 3))
48.0ms
(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

simplify39.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0317702
11544550
25002550

prune197.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes43.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch48.0ms

Steps
ItersRangePoint
9
0.006665254470786589
7065.8830381017015
747.6685893884761
6
-4.314447465097623e+28
-6.322962747029278e+27
-4.227413858499078e+28

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02911
12911

end0.0ms

sample218.0ms

Algorithm
intervals
Results
137.0ms8000×body80valid