Details

Time bar (total: 15.3s)

sample62.0ms

Algorithm
intervals
Results
28.0ms81×body1280valid
12.0ms45×body640valid
9.0ms177×body80valid
4.0ms21×body320valid
1.0ms10×body160valid

simplify34.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
34.0ms
(/ (- (exp x) 1) x)

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize9.0ms

Local error

Found 2 expressions with local error:

3.1b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite31.0ms

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
22.0ms
(/ (- (exp x) 1) x)
9.0ms
(- (exp x) 1)

series68.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
53.0ms
(/ (- (exp x) 1) x)
16.0ms
(- (exp x) 1)

simplify2.0s

Counts
67 → 70
Calls
67 calls:
Slowest
262.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
203.0ms
(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
116.0ms
(* -1 (/ (- 1 (exp x)) x))
86.0ms
(- (pow (exp x) 3) (pow 1 3))
60.0ms
(+ (* 1/2 x) (+ (* 1/6 (pow x 2)) 1))

prune522.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

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×flip3-+ pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in
Counts
3 → 54
Calls
3 calls:
Slowest
28.0ms
(* x (+ (* 1/6 x) 1/2))
9.0ms
(+ (* 1/6 x) 1/2)
7.0ms
(* 1/6 x)

series164.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
89.0ms
(* x (+ (* 1/6 x) 1/2))
59.0ms
(+ (* 1/6 x) 1/2)
15.0ms
(* 1/6 x)

simplify1.2s

Counts
33 → 63
Calls
33 calls:
Slowest
295.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
259.0ms
(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
200.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
75.0ms
(* (exp (* 1/6 x)) (exp 1/2))
56.0ms
(+ (* 1/2 x) (* 1/6 (pow x 2)))

prune439.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b
(log (exp (* x (+ (* 1/6 x) 1/2))))
0.3b
(* 1/6 x)
0.0b
(* x (+ (* 1/6 x) 1/2))
0.0b
(exp (* x (+ (* 1/6 x) 1/2)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×add-log-exp
6×associate-*r* associate-*l*
5×log-prod
4×exp-sum insert-posit16
3×distribute-rgt-in distribute-lft-in log-pow
2×exp-prod exp-to-pow pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×flip3-+ rem-log-exp flip-+ rem-exp-log
Counts
4 → 72
Calls
4 calls:
Slowest
32.0ms
(* x (+ (* 1/6 x) 1/2))
17.0ms
(exp (* x (+ (* 1/6 x) 1/2)))
6.0ms
(* 1/6 x)
4.0ms
(log (exp (* x (+ (* 1/6 x) 1/2))))

series196.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(* x (+ (* 1/6 x) 1/2))
75.0ms
(log (exp (* x (+ (* 1/6 x) 1/2))))
27.0ms
(* 1/6 x)
16.0ms
(exp (* x (+ (* 1/6 x) 1/2)))

simplify3.0s

Counts
47 → 84
Calls
47 calls:
Slowest
312.0ms
(log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))
309.0ms
(exp (* x (+ (* 1/6 x) 1/2)))
272.0ms
(log (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))
265.0ms
(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
254.0ms
(exp (* x (+ (* 1/6 x) 1/2)))

prune817.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

3.4b
(log (* (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))
0.3b
(* 1/6 x)
0.3b
(* 1/6 x)
0.3b
(* 1/6 x)

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
16×add-sqr-sqrt add-exp-log
15×log-pow
10×*-un-lft-identity add-cbrt-cube add-cube-cbrt
9×pow1/3 associate-*r* associate-*l* pow-prod-up
8×pow-prod-down
6×pow-plus prod-exp
4×insert-posit16 add-log-exp
3×rem-log-exp pow-sqr *-commutative cbrt-unprod unswap-sqr
2×pow2
1×log-prod pow3
Counts
4 → 84
Calls
4 calls:
Slowest
66.0ms
(log (* (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))
5.0ms
(* 1/6 x)
5.0ms
(* 1/6 x)
5.0ms
(* 1/6 x)

series203.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(log (* (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))
35.0ms
(* 1/6 x)
27.0ms
(* 1/6 x)
27.0ms
(* 1/6 x)

simplify2.3s

Counts
53 → 96
Calls
53 calls:
Slowest
324.0ms
(log (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))
315.0ms
(* (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))) (cbrt (exp (* x (+ (* 1/6 x) 1/2)))))
310.0ms
(log (* (cbrt (exp (* x (+ (* 1/6 x) 1/2)))) (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))
306.0ms
(+ (log (cbrt (exp (* x (+ (* 1/6 x) 1/2))))) (log (cbrt (exp (* x (+ (* 1/6 x) 1/2))))))
192.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes65.0ms

Accuracy

98.9% (0.2b remaining)

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

bsearch51.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
998.0ms1702×body640valid
985.0ms2250×body1280valid
417.0ms5471×body80valid
166.0ms838×body320valid
67.0ms384×body160valid