Details

Time bar (total: 22.4s)

sample45.0ms

Algorithm
intervals
Results
18.0ms69×body1280valid
10.0ms56×body640valid
6.0ms168×body80valid
3.0ms24×body320valid
1.0ms17×body160valid

simplify17.0ms

Calls
1 calls:
Slowest
17.0ms
(/ (- (exp x) 1) x)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.1b

localize15.0ms

Local error

Found 2 expressions with local error:

4.1b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×associate-/l*
3×*-un-lft-identity add-cube-cbrt
2×pow1 flip3-- add-cbrt-cube difference-of-sqr-1 add-exp-log insert-posit16 flip-- add-log-exp associate-/l/
1×clear-num sub-neg frac-2neg div-sub div-inv
Calls
2 calls:
Slowest
8.0ms
(/ (- (exp x) 1) x)
4.0ms
(- (exp x) 1)

series45.0ms

Calls
2 calls:
Slowest
27.0ms
(/ (- (exp x) 1) x)
18.0ms
(- (exp x) 1)

simplify487.0ms

Calls
13 calls:
Slowest
168.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
122.0ms
(* -1 (/ (- 1 (exp x)) x))
51.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
31.0ms
(- (* (exp x) (exp x)) (* 1 1))
28.0ms
(- (pow (exp x) 3) (pow 1 3))

prune240.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×pow1 add-cbrt-cube associate-*r* add-exp-log insert-posit16 add-log-exp
2×distribute-rgt-in associate-+l+ distribute-lft-in flip3-+ associate-*r/ *-commutative flip-+
1×+-commutative
Calls
3 calls:
Slowest
4.0ms
(+ (* x (+ (* 1/6 x) 1/2)) 1)
3.0ms
(* x (+ (* 1/6 x) 1/2))
0.0ms
(* 1/6 x)

series50.0ms

Calls
3 calls:
Slowest
29.0ms
(* x (+ (* 1/6 x) 1/2))
14.0ms
(+ (* x (+ (* 1/6 x) 1/2)) 1)
7.0ms
(* 1/6 x)

simplify520.0ms

Calls
18 calls:
Slowest
198.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
53.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
51.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
50.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
38.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))

prune284.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

14.1b
(/ (- (* (* x (+ (* 1/6 x) 1/2)) (* x (+ (* 1/6 x) 1/2))) (* 1 1)) (- (* x (+ (* 1/6 x) 1/2)) 1))
0.3b
(* 1/6 x)
0.3b
(* 1/6 x)
0.3b
(* 1/6 x)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
6×add-cbrt-cube add-exp-log
4×pow1 insert-posit16 associate-/l* add-log-exp difference-of-squares
3×associate-/r* *-commutative
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Calls
4 calls:
Slowest
44.0ms
(/ (- (* (* x (+ (* 1/6 x) 1/2)) (* x (+ (* 1/6 x) 1/2))) (* 1 1)) (- (* x (+ (* 1/6 x) 1/2)) 1))
0.0ms
(* 1/6 x)
0.0ms
(* 1/6 x)
0.0ms
(* 1/6 x)

series65.0ms

Calls
4 calls:
Slowest
35.0ms
(/ (- (* (* x (+ (* 1/6 x) 1/2)) (* x (+ (* 1/6 x) 1/2))) (* 1 1)) (- (* x (+ (* 1/6 x) 1/2)) 1))
11.0ms
(* 1/6 x)
11.0ms
(* 1/6 x)
7.0ms
(* 1/6 x)

simplify7.6s

Calls
49 calls:
Slowest
363.0ms
(/ (sqrt (- (* (* x (+ (* 1/6 x) 1/2)) (* x (+ (* 1/6 x) 1/2))) (* 1 1))) (- (* x (+ (* 1/6 x) 1/2)) 1))
359.0ms
(/ (- (* (* x (+ (* 1/6 x) 1/2)) (* x (+ (* 1/6 x) 1/2))) (* 1 1)) (- (* x (+ (* 1/6 x) 1/2)) 1))
325.0ms
(/ (- (* (* x (+ (* 1/6 x) 1/2)) (* x (+ (* 1/6 x) 1/2))) (* 1 1)) (cbrt (- (* x (+ (* 1/6 x) 1/2)) 1)))
318.0ms
(/ (cbrt (- (* (* x (+ (* 1/6 x) 1/2)) (* x (+ (* 1/6 x) 1/2))) (* 1 1))) (- (* x (+ (* 1/6 x) 1/2)) 1))
315.0ms
(/ (cbrt (- (* (* x (+ (* 1/6 x) 1/2)) (* x (+ (* 1/6 x) 1/2))) (* 1 1))) (sqrt (- (* x (+ (* 1/6 x) 1/2)) 1)))

prune569.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

10.4b
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))
10.4b
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))
10.4b
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))
10.4b
(/ (+ (* x (+ (* 1/6 x) 1/2)) 1) (* (cbrt (- (* x (+ (* 1/6 x) 1/2)) 1)) (cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
9×cbrt-prod add-sqr-sqrt *-un-lft-identity flip3-- add-exp-log add-cube-cbrt flip--
8×associate-/r/
7×add-cbrt-cube
4×frac-times pow1 insert-posit16 add-log-exp
3×times-frac pow1/3 associate-/l*
2×cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/l/
1×clear-num associate-/r* frac-2neg flip3-+ prod-exp cbrt-unprod flip-+ div-inv
Calls
4 calls:
Slowest
29.0ms
(/ (+ (* x (+ (* 1/6 x) 1/2)) 1) (* (cbrt (- (* x (+ (* 1/6 x) 1/2)) 1)) (cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))))
12.0ms
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))
7.0ms
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))
7.0ms
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))

series245.0ms

Calls
4 calls:
Slowest
70.0ms
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))
64.0ms
(/ (+ (* x (+ (* 1/6 x) 1/2)) 1) (* (cbrt (- (* x (+ (* 1/6 x) 1/2)) 1)) (cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))))
63.0ms
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))
49.0ms
(cbrt (- (* x (+ (* 1/6 x) 1/2)) 1))

simplify9.4s

Calls
50 calls:
Slowest
955.0ms
(cbrt (- (pow (* x (+ (* 1/6 x) 1/2)) 3) (pow 1 3)))
709.0ms
(+ (pow (* x (+ (* 1/6 x) 1/2)) 3) (pow 1 3))
612.0ms
(cbrt (- (pow (* x (+ (* 1/6 x) 1/2)) 3) (pow 1 3)))
604.0ms
(cbrt (- (pow (* x (+ (* 1/6 x) 1/2)) 3) (pow 1 3)))
336.0ms
(- (+ (/ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x)))))) x) (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x))))))) (* 3 (/ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x)))))) (pow x 2))))

prune712.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.0b

bsearch33.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
796.0ms2277×body1280valid
414.0ms1652×body640valid
338.0ms5455×body80valid
177.0ms844×body320valid
62.0ms409×body160valid