Details

Time bar (total: 14.4s)

sample90.0ms

Algorithm
intervals
Results
37.0ms62×body1280valid
20.0ms60×body640valid
10.0ms24×body2560valid
5.0ms25×body320valid
4.0ms72×body80valid
2.0ms13×body160valid

simplify18.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.3b
(+ x (sqrt (+ (* x x) 1.0)))
3.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
12.8b
(sqrt (+ (* x x) 1.0))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
12.0ms
(+ (* x x) 1.0)
27.0ms
(+ x (sqrt (+ (* x x) 1.0)))
42.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
14.0ms
(sqrt (+ (* x x) 1.0))

series394.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* x x) 1.0)
65.0ms
(+ x (sqrt (+ (* x x) 1.0)))
227.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
68.0ms
(sqrt (+ (* x x) 1.0))

simplify445.0ms

Counts
65 → 65

prune254.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ x (sqrt 1.0)) (- (/ (/ (pow x 3) (pow (sqrt 1.0) 3)) 6) (log (sqrt 1.0))))
0.1b
(/ (/ (pow x 3) (pow (sqrt 1.0) 3)) 6)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
1526×times-frac
691×add-sqr-sqrt
690×*-un-lft-identity
683×add-cube-cbrt
504×unpow-prod-down cube-prod
289×sqrt-prod
220×associate-/l*
120×cube-mult unpow3 sqr-pow
25×add-exp-log
19×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
5×div-inv distribute-lft-out--
3×pow1 cbrt-undiv diff-log associate-/r* difference-of-squares
2×sub-neg flip3-- frac-sub flip-- associate--r+
1×frac-2neg clear-num log-pow associate-/l/ associate--r-
Counts
2 → 930
Calls
2 calls:
1.5s
(- (/ x (sqrt 1.0)) (- (/ (/ (pow x 3) (pow (sqrt 1.0) 3)) 6) (log (sqrt 1.0))))
110.0ms
(/ (/ (pow x 3) (pow (sqrt 1.0) 3)) 6)

series396.0ms

Counts
2 → 6
Calls
2 calls:
215.0ms
(- (/ x (sqrt 1.0)) (- (/ (/ (pow x 3) (pow (sqrt 1.0) 3)) 6) (log (sqrt 1.0))))
181.0ms
(/ (/ (pow x 3) (pow (sqrt 1.0) 3)) 6)

simplify972.0ms

Counts
936 → 936

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x)))
0.0b
(- (+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x))) (* (/ 1.0 8.0) (/ 1 (pow x 3))))
0.1b
(/ 1 (pow x 3))
11.2b
(log (- (+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x))) (* (/ 1.0 8.0) (/ 1 (pow x 3)))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
30×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×frac-sub
14×add-exp-log
12×unpow-prod-down cube-prod associate-/r*
11×add-log-exp
10×log-div
9×flip3-+ flip-+
6×div-exp add-cbrt-cube
5×pow1
4×cube-mult frac-times unpow3 associate-*r/ associate-*l/ un-div-inv sqr-pow
3×pow-to-exp rec-exp log-prod 1-exp pow-exp associate-/l*
2×flip3-- diff-log sum-log flip--
1×cbrt-undiv +-commutative sub-neg pow-flip frac-2neg rem-log-exp associate--l+ clear-num log-pow div-inv inv-pow
Counts
4 → 128
Calls
4 calls:
13.0ms
(+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x)))
65.0ms
(- (+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x))) (* (/ 1.0 8.0) (/ 1 (pow x 3))))
15.0ms
(/ 1 (pow x 3))
49.0ms
(log (- (+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x))) (* (/ 1.0 8.0) (/ 1 (pow x 3)))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x)))
54.0ms
(- (+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x))) (* (/ 1.0 8.0) (/ 1 (pow x 3))))
48.0ms
(/ 1 (pow x 3))
230.0ms
(log (- (+ (* 2 x) (* (/ 1.0 2.0) (/ 1 x))) (* (/ 1.0 8.0) (/ 1 (pow x 3)))))

simplify1.2s

Counts
140 → 140

prune406.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (pow x 5))
0.1b
(/ 1 (pow x 3))
12.9b
(log (- (* (/ 1.0 8.0) (/ 1 (pow x 3))) (+ (* (/ 1.0 2.0) (/ 1 x)) (* (/ 1.0 16.0) (/ 1 (pow x 5))))))
18.7b
(- (* (/ 1.0 8.0) (/ 1 (pow x 3))) (+ (* (/ 1.0 2.0) (/ 1 x)) (* (/ 1.0 16.0) (/ 1 (pow x 5)))))

rewrite557.0ms

Algorithm
rewrite-expression-head
Rules
144×frac-sub
128×frac-add
100×frac-times associate-*r/ associate-*l/ un-div-inv
74×log-div
57×times-frac
46×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
23×add-exp-log
19×associate-/r*
12×cube-prod div-exp
9×add-log-exp
8×flip3-+ add-cbrt-cube flip-+ sqr-pow
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
5×pow1
4×cube-mult unpow3
3×log-prod
2×cbrt-undiv flip3-- pow-flip frac-2neg diff-log clear-num flip-- div-inv inv-pow
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 298
Calls
4 calls:
9.0ms
(/ 1 (pow x 5))
11.0ms
(/ 1 (pow x 3))
95.0ms
(log (- (* (/ 1.0 8.0) (/ 1 (pow x 3))) (+ (* (/ 1.0 2.0) (/ 1 x)) (* (/ 1.0 16.0) (/ 1 (pow x 5))))))
53.0ms
(- (* (/ 1.0 8.0) (/ 1 (pow x 3))) (+ (* (/ 1.0 2.0) (/ 1 x)) (* (/ 1.0 16.0) (/ 1 (pow x 5)))))

series466.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1 (pow x 5))
47.0ms
(/ 1 (pow x 3))
260.0ms
(log (- (* (/ 1.0 8.0) (/ 1 (pow x 3))) (+ (* (/ 1.0 2.0) (/ 1 x)) (* (/ 1.0 16.0) (/ 1 (pow x 5))))))
87.0ms
(- (* (/ 1.0 8.0) (/ 1 (pow x 3))) (+ (* (/ 1.0 2.0) (/ 1 x)) (* (/ 1.0 16.0) (/ 1 (pow x 5)))))

simplify794.0ms

Counts
310 → 310

prune891.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch133.0ms

Steps
ItersRangePoint
10
1.5244367550608482e-07
9556.682540875734
0.8981400227354687
9
-1501.2167507114543
-0.006495210018506858
-1.017049376431383

simplify489.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.5s2224×body1280valid
560.0ms1649×body640valid
335.0ms836×body2560valid
163.0ms820×body320valid
148.0ms2075×body80valid
45.0ms396×body160valid