Details

Time bar (total: 20.1s)

sample93.0ms

Algorithm
intervals
Results
40.0ms82×body1280valid
24.0ms78×body10240exit
9.0ms32×body640valid
5.0ms102×body80valid
4.0ms26×body320valid
2.0ms14×body160valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(/ (exp x) (- (exp x) 1))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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
13.0ms
(/ (exp x) (- (exp x) 1))
7.0ms
(- (exp x) 1)

series67.0ms

Calls
2 calls:
Slowest
44.0ms
(/ (exp x) (- (exp x) 1))
23.0ms
(- (exp x) 1)

simplify1.1s

Calls
41 calls:
Slowest
352.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
144.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
53.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
50.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
34.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (sqrt (- (exp x) 1)))

prune346.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

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
16.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
1.0ms
(* 1/12 x)

series52.0ms

Calls
2 calls:
Slowest
26.0ms
(* 1/12 x)
26.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

simplify177.0ms

Calls
7 calls:
Slowest
66.0ms
(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
36.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
32.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
28.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
6.0ms
(* 1/12 x)

prune239.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

4.1b
(- (pow (exp x) 3) (pow 1 3))
0.0b
(* (/ (exp x) (- (pow (exp x) 3) (pow 1 3))) (+ 1 (* (exp x) (+ 1 (exp x)))))
0.0b
(pow (exp x) 3)
0.0b
(* (exp x) (+ 1 (exp x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
36×associate-*l*
34×*-un-lft-identity
27×times-frac
22×add-cube-cbrt
12×add-cbrt-cube difference-of-squares
9×pow1 add-exp-log
8×distribute-lft-out--
7×unpow-prod-down cube-prod
6×associate-*r* add-log-exp
5×cube-mult
4×difference-cubes associate-*r/ insert-posit16
3×flip3-+ prod-exp cbrt-unprod flip-+
2×distribute-rgt-in frac-times distribute-lft-in flip3-- pow-prod-down associate-/r/ *-commutative flip--
1×pow-to-exp cbrt-undiv sub-neg pow-pow diff-log unpow3 div-exp associate-*l/ pow-exp div-inv rem-cube-cbrt
Calls
4 calls:
Slowest
18.0ms
(* (/ (exp x) (- (pow (exp x) 3) (pow 1 3))) (+ 1 (* (exp x) (+ 1 (exp x)))))
8.0ms
(- (pow (exp x) 3) (pow 1 3))
5.0ms
(* (exp x) (+ 1 (exp x)))
1.0ms
(pow (exp x) 3)

series231.0ms

Calls
4 calls:
Slowest
121.0ms
(* (/ (exp x) (- (pow (exp x) 3) (pow 1 3))) (+ 1 (* (exp x) (+ 1 (exp x)))))
43.0ms
(- (pow (exp x) 3) (pow 1 3))
37.0ms
(* (exp x) (+ 1 (exp x)))
30.0ms
(pow (exp x) 3)

simplify8.9s

Calls
93 calls:
Slowest
1.1s
(/ (* (+ (pow (exp x) 2) (+ (exp x) 1)) (exp x)) (- (pow (exp x) 3) 1))
703.0ms
(* (- (pow (exp x) 3) (pow 1 3)) (- 1 (* (exp x) (+ 1 (exp x)))))
675.0ms
(/ (* (+ (pow (exp x) 2) (+ (exp x) 1)) (exp x)) (- (pow (exp x) 3) 1))
425.0ms
(* (exp x) (+ (pow 1 3) (pow (* (exp x) (+ 1 (exp x))) 3)))
415.0ms
(* (/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (pow (exp x) 3) (pow 1 3)) (- (pow (exp x) 3) (pow 1 3))) (- (pow (exp x) 3) (pow 1 3)))) (* (* (+ 1 (* (exp x) (+ 1 (exp x)))) (+ 1 (* (exp x) (+ 1 (exp x))))) (+ 1 (* (exp x) (+ 1 (exp x))))))

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

4.1b
(- (pow (exp x) 3) (pow 1 3))
0.6b
(cbrt (* (exp x) (+ 1 (exp x))))
0.6b
(cbrt (* (exp x) (+ 1 (exp x))))
0.6b
(cbrt (* (exp x) (+ 1 (exp x))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
7×*-un-lft-identity
6×cbrt-div associate-*r/ add-log-exp
4×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
3×cbrt-prod flip3-+ pow1/3 flip-+ difference-of-squares
2×distribute-lft-out--
1×cube-mult difference-cubes sub-neg unpow-prod-down flip3-- diff-log cube-prod flip--
Calls
4 calls:
Slowest
8.0ms
(- (pow (exp x) 3) (pow 1 3))
6.0ms
(cbrt (* (exp x) (+ 1 (exp x))))
3.0ms
(cbrt (* (exp x) (+ 1 (exp x))))
3.0ms
(cbrt (* (exp x) (+ 1 (exp x))))

series508.0ms

Calls
4 calls:
Slowest
185.0ms
(cbrt (* (exp x) (+ 1 (exp x))))
170.0ms
(cbrt (* (exp x) (+ 1 (exp x))))
117.0ms
(cbrt (* (exp x) (+ 1 (exp x))))
36.0ms
(- (pow (exp x) 3) (pow 1 3))

simplify1.9s

Calls
32 calls:
Slowest
238.0ms
(+ (* 3 x) (+ (* 9/2 (pow x 3)) (* 9/2 (pow x 2))))
225.0ms
(+ (* 1/6 (* (pow x 2) (pow 2 1/3))) (+ (* 1/2 (* x (pow 2 1/3))) (pow 2 1/3)))
182.0ms
(+ (* 1/6 (* (pow x 2) (pow 2 1/3))) (+ (* 1/2 (* x (pow 2 1/3))) (pow 2 1/3)))
160.0ms
(+ (* 1/6 (* (pow x 2) (pow 2 1/3))) (+ (* 1/2 (* x (pow 2 1/3))) (pow 2 1/3)))
86.0ms
(cbrt (* (exp x) (- (* 1 1) (* (exp x) (exp x)))))

prune920.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 21.4b

bsearch35.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.4s2576×body10240exit
1.2s2336×body1280valid
467.0ms1530×body640valid
259.0ms2857×body80valid
208.0ms882×body320valid
51.0ms395×body160valid