Details

Time bar (total: 12.3s)

sample79.0ms

Algorithm
intervals
Results
34.0ms62×body1280valid
16.0ms50×body640valid
9.0ms24×body2560valid
7.0ms34×body320valid
4.0ms75×body80valid
1.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
3.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.9b
(sqrt (+ (* x x) 1.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u fma-def flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow hypot-def
Counts
3 → 52
Calls
3 calls:
9.0ms
(+ x (sqrt (+ (* x x) 1.0)))
12.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series278.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
173.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0331422
11127385
25002366

prune182.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv expm1-log1p-u associate-*r/ pow-prod-down *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 272
Calls
1 calls:
76.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series143.0ms

Counts
1 → 3
Calls
1 calls:
143.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify93.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07291769
138381380
250031380

prune375.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (- 0.125) (/ 1 (pow x 3)) (fma x 2 (/ 0.5 x)))
0.0b
(fma x 2 (/ 0.5 x))
0.2b
(/ 1 (pow x 3))
10.2b
(log (fma (- 0.125) (/ 1 (pow x 3)) (fma x 2 (/ 0.5 x))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
30×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×add-exp-log
12×unpow-prod-down cube-prod associate-/r*
6×div-exp add-cbrt-cube
5×pow1
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp rec-exp log-prod 1-exp pow-exp associate-/l*
2×fma-udef
1×cbrt-undiv pow-flip frac-2neg rem-log-exp clear-num log-pow div-inv inv-pow
Counts
4 → 109
Calls
4 calls:
0.0ms
(fma (- 0.125) (/ 1 (pow x 3)) (fma x 2 (/ 0.5 x)))
0.0ms
(fma x 2 (/ 0.5 x))
5.0ms
(/ 1 (pow x 3))
1.0ms
(log (fma (- 0.125) (/ 1 (pow x 3)) (fma x 2 (/ 0.5 x))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma (- 0.125) (/ 1 (pow x 3)) (fma x 2 (/ 0.5 x)))
57.0ms
(fma x 2 (/ 0.5 x))
33.0ms
(/ 1 (pow x 3))
159.0ms
(log (fma (- 0.125) (/ 1 (pow x 3)) (fma x 2 (/ 0.5 x))))

simplify44.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0325651
11502518
25001517

prune214.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
11.7b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite845.0ms

Algorithm
rewrite-expression-head
Rules
2802×times-frac
2496×add-sqr-sqrt
1944×*-un-lft-identity
1522×prod-diff
1510×add-cube-cbrt
965×associate--r+
652×unpow-prod-down
339×distribute-rgt-neg-in
330×difference-of-squares
297×distribute-lft-neg-in
272×sqr-pow
149×cube-prod
134×distribute-lft-out--
104×div-inv
99×neg-mul-1
49×cube-mult unpow3
40×fma-neg
19×associate-/r*
15×add-exp-log
13×associate-/l*
12×log-prod
9×add-log-exp
8×frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 1793
Calls
4 calls:
6.0ms
(/ (- 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
263.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
348.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
187.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
56.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify427.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500248960

prune6.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.8b

bsearch83.0ms

Steps
ItersRangePoint
9
0.8894813891870064
5702493.407928515
0.9005070813731784
8
-1.3862719480695398
-4.2961337728369966e-05
-1.0059580948780908

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04427
14427

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s2367×body1280valid
469.0ms1530×body640valid
288.0ms785×body2560valid
154.0ms788×body320valid
115.0ms2137×body80valid
48.0ms393×body160valid