Details

Time bar (total: 7.1s)

sample62.0ms

Algorithm
intervals
Results
33.0ms68×body1280valid
11.0ms46×body640valid
3.0ms110×body80valid
3.0ms23×body320valid
1.0ms80×body80nan
1.0ms9×body160valid

simplify3.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize4.0ms

Local error

Found 1 expressions with local error:

2.7b
(log (+ 1.0 x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod *-un-lft-identity
2×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-div
1×flip3-+ rem-log-exp log-pow add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
1 → 15
Calls
1 calls:
5.0ms
(log (+ 1.0 x))

series58.0ms

Counts
1 → 3
Calls
1 calls:
58.0ms
(log (+ 1.0 x))

simplify34.0ms

Counts
18 → 18

prune39.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
2×diff-log associate-*r/ frac-sub
1×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt sub-neg flip3-- *-un-lft-identity flip3-+ associate--l+ sum-log add-cbrt-cube flip-- flip-+
Counts
1 → 16
Calls
1 calls:
54.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

series47.0ms

Counts
1 → 3
Calls
1 calls:
47.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

simplify117.0ms

Counts
19 → 19

prune57.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
13.3b
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
38.2b
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
533×add-exp-log
341×prod-exp
199×div-exp
132×pow-to-exp pow-exp
99×associate-*r/
48×frac-sub
42×pow1
41×frac-times add-cbrt-cube
38×flip3-+ flip-+
29×associate-*l/
26×associate-/l/
21×cbrt-unprod
17×pow-prod-down
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
7×cbrt-undiv
5×add-log-exp difference-of-squares
4×associate-/r/ pow-sqr pow-prod-up associate-/l*
3×associate-/r*
2×flip3-- pow-plus frac-add associate--l+ flip--
1×pow2 distribute-rgt-in sub-neg frac-2neg distribute-lft-in diff-log div-sub swap-sqr associate-*r* associate-*l* clear-num *-commutative div-inv
Counts
3 → 260
Calls
3 calls:
83.0ms
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
42.0ms
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
130.0ms
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series337.0ms

Counts
3 → 9
Calls
3 calls:
89.0ms
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
96.0ms
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
152.0ms
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify146.0ms

Counts
269 → 269

prune506.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))
0.7b
(log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))))
13.3b
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2))))))
31.7b
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
812×times-frac
732×add-sqr-sqrt
470×unpow-prod-down
338×sqr-pow
336×unpow2
289×unswap-sqr
267×add-exp-log
181×div-exp
149×add-cube-cbrt *-un-lft-identity
121×pow-to-exp pow-exp
100×prod-exp
68×swap-sqr associate-*r* associate-*l*
18×add-cbrt-cube
14×log-prod
11×pow1
7×associate--r+
5×cbrt-undiv div-inv add-log-exp difference-of-squares
4×associate-/r/ cbrt-unprod associate-/l*
3×associate-*r/ rem-log-exp associate-/r*
2×flip3-- flip3-+ frac-add associate--l+ flip-- flip-+ associate-/l/
1×pow2 distribute-rgt-in frac-times sub-neg frac-2neg distribute-lft-in pow-plus diff-log div-sub pow-prod-down associate-*l/ clear-num pow-sqr log-pow *-commutative pow-prod-up
Counts
4 → 691
Calls
4 calls:
112.0ms
(* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))
7.0ms
(log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))))
36.0ms
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2))))))
112.0ms
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))
706.0ms
(log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))))
103.0ms
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2))))))
470.0ms
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (log (pow (exp 1/4) (* (/ (pow x 2) (pow 1.0 2)) (/ (pow x 2) (pow 1.0 2)))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify128.0ms

Counts
703 → 703

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes70.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 22.1b

bsearch1.0ms

simplify1.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s2248×body1280valid
400.0ms1665×body640valid
105.0ms2680×body80nan
97.0ms778×body320valid
73.0ms2858×body80valid
31.0ms451×body160valid