Details

Time bar (total: 18.3s)

sample89.0ms

Algorithm
intervals
Results
39.0ms72×body1280valid
19.0ms50×body640valid
9.0ms25×body2560valid
5.0ms28×body320valid
3.0ms73×body80valid
1.0ms8×body160valid

simplify14.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (+ (* x x) 1.0)))
3.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
16.5b
(sqrt (+ (* x x) 1.0))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
34.0ms
(+ x (sqrt (+ (* x x) 1.0)))
60.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
20.0ms
(sqrt (+ (* x x) 1.0))

series739.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(+ x (sqrt (+ (* x x) 1.0)))
597.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
64.0ms
(sqrt (+ (* x x) 1.0))

simplify1.7s

Counts
51 → 51

prune235.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite426.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
279.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
127.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series365.0ms

Counts
2 → 6
Calls
2 calls:
190.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
175.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.7s

Counts
292 → 292

prune557.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))
0.2b
(* (sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
5.2b
(sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
5.2b
(sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
240×times-frac
226×associate-*r*
208×add-sqr-sqrt
140×unpow-prod-down cube-prod
130×add-cube-cbrt *-un-lft-identity
104×sqrt-prod
48×sqrt-div
40×sqr-pow
30×cube-mult unpow3
29×add-exp-log associate-*r/ unswap-sqr
24×frac-sub
23×pow1
16×frac-times
12×flip3-- flip3-+ flip-- flip-+
11×prod-exp add-cbrt-cube
10×sqrt-pow1 pow1/2
9×div-exp associate-*l*
8×swap-sqr
6×pow-to-exp pow-exp
5×pow-prod-up
4×pow-prod-down associate-*l/ add-log-exp
3×pow-sqr cbrt-unprod
2×rem-sqrt-square *-commutative
1×cbrt-undiv pow2 pow-plus sqrt-unprod rem-square-sqrt div-inv
Counts
4 → 377
Calls
4 calls:
141.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))
752.0ms
(* (sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
132.0ms
(sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
140.0ms
(sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

series931.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))
250.0ms
(* (sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
254.0ms
(sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
238.0ms
(sqrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

simplify510.0ms

Counts
389 → 389

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (/ (- 0.125) (pow x 3)) (/ 0.5 x)) (* 2 x))
0.0b
(+ (/ (- 0.125) (pow x 3)) (/ 0.5 x))
0.4b
(/ (- 0.125) (pow x 3))
9.2b
(log (+ (+ (/ (- 0.125) (pow x 3)) (/ 0.5 x)) (* 2 x)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
124×times-frac
87×*-un-lft-identity
77×add-sqr-sqrt add-cube-cbrt
40×distribute-rgt-neg-in
39×distribute-lft-neg-in
33×unpow-prod-down cube-prod
13×neg-mul-1
12×associate-/r*
11×cube-mult unpow3 add-log-exp sqr-pow
10×add-exp-log associate-/l*
6×add-cbrt-cube
5×pow1
4×sum-log
3×neg-sub0 associate-+l- log-prod flip3-+ div-sub div-exp flip-+ distribute-lft-out
2×+-commutative log-div
1×cbrt-undiv pow-to-exp associate-+l+ frac-2neg distribute-frac-neg rem-log-exp frac-add pow-exp clear-num log-pow div-inv
Counts
4 → 202
Calls
4 calls:
863.0ms
(+ (+ (/ (- 0.125) (pow x 3)) (/ 0.5 x)) (* 2 x))
166.0ms
(+ (/ (- 0.125) (pow x 3)) (/ 0.5 x))
15.0ms
(/ (- 0.125) (pow x 3))
407.0ms
(log (+ (+ (/ (- 0.125) (pow x 3)) (/ 0.5 x)) (* 2 x)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ (+ (/ (- 0.125) (pow x 3)) (/ 0.5 x)) (* 2 x))
115.0ms
(+ (/ (- 0.125) (pow x 3)) (/ 0.5 x))
50.0ms
(/ (- 0.125) (pow x 3))
205.0ms
(log (+ (+ (/ (- 0.125) (pow x 3)) (/ 0.5 x)) (* 2 x)))

simplify1.2s

Counts
214 → 214

prune543.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes100.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch128.0ms

Steps
ItersRangePoint
6
0.1443711673119872
1.2364512583087228
0.8895218929182532
11
-31.62993370098301
-4.221128360075206e-33
-1.000827500383001

simplify1.4s

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s2287×body1280valid
595.0ms1538×body640valid
498.0ms2141×body80valid
367.0ms844×body2560valid
188.0ms776×body320valid
44.0ms414×body160valid