Details

Time bar (total: 19.7s)

sample100.0ms

Algorithm
intervals
Results
31.0ms65×body1280valid
27.0ms70×body10240exit
19.0ms57×body640valid
6.0ms90×body80valid
6.0ms27×body320valid
2.0ms17×body160valid

simplify10.0ms

Calls
1 calls:
Slowest
9.0ms
(/ (exp x) (- (exp x) 1))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize8.0ms

Local error

Found 2 expressions with local error:

4.8b
(- (exp x) 1)
0.5b
(/ (exp x) (- (exp x) 1))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×times-frac
11×*-un-lft-identity add-cube-cbrt
5×difference-of-sqr-1
4×associate-/r* add-cbrt-cube
3×add-exp-log associate-/l*
2×pow1 flip3-- associate-/r/ insert-posit16 flip-- add-log-exp
1×cbrt-undiv clear-num sub-neg frac-2neg div-exp div-inv
Calls
2 calls:
Slowest
10.0ms
(/ (exp x) (- (exp x) 1))
4.0ms
(- (exp x) 1)

series62.0ms

Calls
2 calls:
Slowest
34.0ms
(- (exp x) 1)
28.0ms
(/ (exp x) (- (exp x) 1))

simplify1.1s

Calls
41 calls:
Slowest
343.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
149.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
43.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
41.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
41.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune421.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x 1/6)
0.1b
(* (+ 1/2 (* x 1/6)) (* x x))
0.0b
(/ (exp x) (+ x (* (+ 1/2 (* x 1/6)) (* x x))))
0.0b
(+ x (* (+ 1/2 (* x 1/6)) (* x x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
8×add-cbrt-cube
7×add-exp-log
6×pow1
4×insert-posit16 add-log-exp
3×associate-/r* flip3-+ associate-*l* flip-+ associate-/l*
2×associate-*l/ associate-/r/ *-commutative
1×cbrt-undiv +-commutative clear-num frac-2neg div-exp associate-*r* pow-prod-down prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
11.0ms
(* (+ 1/2 (* x 1/6)) (* x x))
9.0ms
(/ (exp x) (+ x (* (+ 1/2 (* x 1/6)) (* x x))))
4.0ms
(+ x (* (+ 1/2 (* x 1/6)) (* x x)))
1.0ms
(* x 1/6)

series82.0ms

Calls
4 calls:
Slowest
36.0ms
(* (+ 1/2 (* x 1/6)) (* x x))
22.0ms
(/ (exp x) (+ x (* (+ 1/2 (* x 1/6)) (* x x))))
13.0ms
(+ x (* (+ 1/2 (* x 1/6)) (* x x)))
11.0ms
(* x 1/6)

simplify5.4s

Calls
46 calls:
Slowest
402.0ms
(* (+ (pow 1/2 3) (pow (* x 1/6) 3)) (* x x))
325.0ms
(- (+ (* 18 (/ (exp x) (pow x 5))) (* 6 (/ (exp x) (pow x 3)))) (* 18 (/ (exp x) (pow x 4))))
250.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (+ x (* (+ 1/2 (* x 1/6)) (* x x))) (+ x (* (+ 1/2 (* x 1/6)) (* x x)))) (+ x (* (+ 1/2 (* x 1/6)) (* x x)))))
230.0ms
(- (+ (* 18 (/ (exp x) (pow x 5))) (* 6 (/ (exp x) (pow x 3)))) (* 18 (/ (exp x) (pow x 4))))
220.0ms
(- x (* (+ 1/2 (* x 1/6)) (* x x)))

prune651.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b
(* 1/12 x)
0.0b
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
2×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×+-commutative associate-+r+ sum-log flip3-+ *-commutative flip-+
Calls
2 calls:
Slowest
11.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.0ms
(* 1/12 x)

series15.0ms

Calls
2 calls:
Slowest
7.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
7.0ms
(* 1/12 x)

simplify158.0ms

Calls
7 calls:
Slowest
65.0ms
(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
30.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
26.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
22.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
6.0ms
(* 1/12 x)

prune187.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.6b
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.6b
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.5b
(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1 flip3-+ flip-+
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
57.0ms
(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
15.0ms
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
12.0ms
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
12.0ms
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))

series235.0ms

Calls
4 calls:
Slowest
74.0ms
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
59.0ms
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
59.0ms
(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
42.0ms
(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

simplify6.7s

Calls
59 calls:
Slowest
406.0ms
(- (+ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) (* 2 (/ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) x))) (* 8/3 (/ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) (pow x 3))))
382.0ms
(* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
373.0ms
(* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
369.0ms
(- (+ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) (* 2 (/ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) x))) (* 8/3 (/ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) (pow x 3))))
352.0ms
(- (+ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) (* 2 (/ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) x))) (* 8/3 (/ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) (pow x 3))))

prune746.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

regimes102.0ms

Accuracy

0% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 1.1b

bsearch3.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2248×body1280valid
1.0s2543×body10240exit
471.0ms1616×body640valid
240.0ms2868×body80valid
153.0ms832×body320valid
54.0ms438×body160valid