Details

Time bar (total: 16.3s)

sample89.0ms

Algorithm
intervals
Results
35.0ms67×body1280valid
21.0ms57×body640valid
12.0ms172×body80valid
7.0ms28×body320valid
2.0ms13×body160valid

simplify47.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
47.0ms
(/ (- (exp x) 1) x)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize8.0ms

Local error

Found 2 expressions with local error:

4.5b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity
21×times-frac
14×add-cube-cbrt
10×difference-of-squares
7×associate-/l*
5×difference-of-sqr-1 distribute-lft-out--
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r*
2×pow1 flip3-- insert-posit16 flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
2 → 64
Calls
2 calls:
Slowest
30.0ms
(/ (- (exp x) 1) x)
8.0ms
(- (exp x) 1)

series64.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
42.0ms
(/ (- (exp x) 1) x)
22.0ms
(- (exp x) 1)

simplify2.0s

Counts
67 → 70
Calls
67 calls:
Slowest
211.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
189.0ms
(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
137.0ms
(* -1 (/ (- 1 (exp x)) x))
74.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))
67.0ms
(- (pow (exp x) 3) (pow 1 3))

prune569.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×add-log-exp
3×insert-posit16
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative sum-log
Counts
3 → 56
Calls
3 calls:
Slowest
40.0ms
(* x (+ (* 1/6 x) 1/2))
11.0ms
(+ 1 (* x (+ (* 1/6 x) 1/2)))
9.0ms
(* 1/6 x)

series165.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
112.0ms
(* x (+ (* 1/6 x) 1/2))
27.0ms
(* 1/6 x)
26.0ms
(+ 1 (* x (+ (* 1/6 x) 1/2)))

simplify1.4s

Counts
35 → 65
Calls
35 calls:
Slowest
265.0ms
(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
224.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
190.0ms
(* (exp 1) (exp (* x (+ (* 1/6 x) 1/2))))
162.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
83.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))

prune524.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-log-exp
6×*-un-lft-identity associate-*l* add-cube-cbrt
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×sum-log insert-posit16
2×*-commutative
1×+-commutative associate-+l+ flip3-+ flip-+ unswap-sqr
Counts
3 → 52
Calls
3 calls:
Slowest
30.0ms
(+ (+ 1 (* x (* 1/6 x))) (* x 1/2))
24.0ms
(* x (* 1/6 x))
14.0ms
(* 1/6 x)

series95.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
35.0ms
(* x (* 1/6 x))
35.0ms
(+ (+ 1 (* x (* 1/6 x))) (* x 1/2))
26.0ms
(* 1/6 x)

simplify1.8s

Counts
28 → 61
Calls
28 calls:
Slowest
332.0ms
(* (* (* x x) x) (* (* (* 1/6 x) (* 1/6 x)) (* 1/6 x)))
315.0ms
(* (* (exp 1) (exp (* x (* 1/6 x)))) (exp (* x 1/2)))
253.0ms
(* (* (* x x) x) (* (* (* 1/6 1/6) 1/6) (* (* x x) x)))
236.0ms
(* (exp (+ 1 (* x (* 1/6 x)))) (exp (* x 1/2)))
211.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))

prune534.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

9.2b
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
9.2b
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
9.2b
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
0.3b
(* 1/6 x)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×cbrt-prod *-un-lft-identity add-cube-cbrt
6×pow1 cbrt-div add-cbrt-cube add-exp-log
4×insert-posit16 add-log-exp
3×flip3-+ pow1/3 associate-*r* associate-*l* flip-+
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 61
Calls
4 calls:
Slowest
17.0ms
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
17.0ms
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
16.0ms
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
11.0ms
(* 1/6 x)

series264.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
87.0ms
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
69.0ms
(cbrt (+ (+ 1 (* x (* 1/6 x))) (* x 1/2)))
15.0ms
(* 1/6 x)

simplify4.9s

Counts
36 → 73
Calls
36 calls:
Slowest
777.0ms
(cbrt (- (* (+ 1 (* x (* 1/6 x))) (+ 1 (* x (* 1/6 x)))) (* (* x 1/2) (* x 1/2))))
362.0ms
(+ (/ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x)))))) x) (+ (/ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x)))))) (pow x 2)) (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x))))))))
340.0ms
(+ (/ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x)))))) x) (+ (/ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x)))))) (pow x 2)) (exp (* 1/3 (- (log 1/6) (* 2 (log (/ -1 x))))))))
337.0ms
(cbrt (- (* (+ 1 (* x (* 1/6 x))) (+ 1 (* x (* 1/6 x)))) (* (* x 1/2) (* x 1/2))))
337.0ms
(+ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ 1 x)))))) (+ (/ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ 1 x)))))) x) (/ (exp (* 1/3 (- (log 1/6) (* 2 (log (/ 1 x)))))) (pow x 2))))

prune843.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes79.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.0b

bsearch40.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.1s2252×body1280valid
649.0ms1715×body640valid
381.0ms5443×body80valid
265.0ms844×body320valid
55.0ms379×body160valid