Details

Time bar (total: 46.8s)

sample320.0ms

Algorithm
intervals
Results
106.0ms59×body1280valid
89.0ms69×body10240exit
59.0ms349×body80valid
26.0ms43×body640valid
11.0ms21×body320valid
5.0ms14×body160valid

simplify346.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
345.0ms
(/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2)

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize49.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b
(* x (- -1 eps))
0.0b
(* x (- -1 eps))
0.0b
(/ (exp (* x (+ eps -1))) eps)

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
28×add-sqr-sqrt
18×add-cube-cbrt
16×add-log-exp
15×times-frac
10×add-cbrt-cube associate-*r*
9×add-exp-log
8×distribute-rgt-in pow1 distribute-lft-in exp-sum distribute-lft-out--
6×sub-neg diff-log associate-*l*
5×flip3-- flip-- associate-/l*
4×associate-*r/ frac-sub insert-posit16
3×associate-/r* difference-of-squares
2×sum-log flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out associate--r+ unswap-sqr
1×cbrt-undiv clear-num frac-2neg div-exp associate--l+ div-inv associate--r-
Counts
4 → 119
Calls
4 calls:
Slowest
161.0ms
(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
28.0ms
(* x (- -1 eps))
18.0ms
(* x (- -1 eps))
8.0ms
(/ (exp (* x (+ eps -1))) eps)

series337.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
65.0ms
(* x (- -1 eps))
61.0ms
(* x (- -1 eps))
35.0ms
(/ (exp (* x (+ eps -1))) eps)

simplify17.4s

Counts
108 → 131
Calls
108 calls:
Slowest
797.0ms
(- (* (+ (pow (exp (* x (+ eps -1))) 3) (pow (/ (exp (* x (+ eps -1))) eps) 3)) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (+ (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (- (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps)) (* (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
671.0ms
(- (* (- (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps))) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (- (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
583.0ms
(/ (* (cbrt (exp (* x (+ eps -1)))) (cbrt (exp (* x (+ eps -1))))) (sqrt eps))
514.0ms
(* (* (* x x) x) (* (* (- -1 eps) (- -1 eps)) (- -1 eps)))
511.0ms
(/ (* (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (exp (* x (+ eps -1)))) (* (* eps eps) eps))

prune1.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 3 expressions with local error:

5.6b
(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
0.1b
(* (* x (* x x)) -2/3)
0.1b
(* x (* x x))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
17×add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
8×add-log-exp
6×add-sqr-sqrt
5×*-un-lft-identity pow-prod-up add-cube-cbrt
4×associate-*r* associate-*l*
3×diff-log insert-posit16
2×sub-neg associate--l+ *-commutative
1×associate--l- pow2 pow-plus flip3-- cube-unmult pow-sqr flip-- unswap-sqr
Counts
3 → 64
Calls
3 calls:
Slowest
72.0ms
(* (* x (* x x)) -2/3)
54.0ms
(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
26.0ms
(* x (* x x))

series166.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
58.0ms
(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
57.0ms
(* (* x (* x x)) -2/3)
51.0ms
(* x (* x x))

simplify3.9s

Counts
36 → 73
Calls
36 calls:
Slowest
571.0ms
(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
566.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
465.0ms
(/ (/ (exp 2) (exp (* x x))) (exp (* (* x (* x x)) -2/3)))
382.0ms
(* (* (* (* x (* x x)) (* x (* x x))) (* x (* x x))) (* (* -2/3 -2/3) -2/3))
253.0ms
(* (* (* (* x x) x) (* (* (* x x) (* x x)) (* x x))) (* (* -2/3 -2/3) -2/3))

prune678.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 3 expressions with local error:

5.6b
(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
0.1b
(* (* x (* x x)) -2/3)
0.1b
(* x (* x x))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
17×add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
8×add-log-exp
6×add-sqr-sqrt
5×*-un-lft-identity pow-prod-up add-cube-cbrt
4×associate-*r* associate-*l*
3×diff-log insert-posit16
2×sub-neg associate--l+ *-commutative
1×associate--l- pow2 pow-plus flip3-- cube-unmult pow-sqr flip-- unswap-sqr
Counts
3 → 64
Calls
3 calls:
Slowest
46.0ms
(* (* x (* x x)) -2/3)
43.0ms
(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
13.0ms
(* x (* x x))

series149.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
61.0ms
(* (* x (* x x)) -2/3)
50.0ms
(* x (* x x))
37.0ms
(- (- 2 (* x x)) (* (* x (* x x)) -2/3))

simplify3.9s

Counts
36 → 73
Calls
36 calls:
Slowest
531.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
479.0ms
(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
421.0ms
(/ (/ (exp 2) (exp (* x x))) (exp (* (* x (* x x)) -2/3)))
402.0ms
(* (* (* (* x (* x x)) (* x (* x x))) (* x (* x x))) (* (* -2/3 -2/3) -2/3))
285.0ms
(* (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x))) (* (* -2/3 -2/3) -2/3))

prune560.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

7.0b
(+ (* x x) (* (* x (* x x)) -2/3))
0.1b
(* (* x (* x x)) -2/3)
0.1b
(* x (* x x))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
17×add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
6×add-sqr-sqrt
5×*-un-lft-identity pow-prod-up add-cube-cbrt add-log-exp
4×associate-*r* associate-*l*
3×insert-posit16
2×*-commutative
1×pow2 +-commutative sum-log flip3-+ pow-plus cube-unmult pow-sqr flip-+ unswap-sqr
Counts
3 → 59
Calls
3 calls:
Slowest
58.0ms
(* (* x (* x x)) -2/3)
26.0ms
(* x (* x x))
12.0ms
(+ (* x x) (* (* x (* x x)) -2/3))

series216.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
107.0ms
(+ (* x x) (* (* x (* x x)) -2/3))
66.0ms
(* (* x (* x x)) -2/3)
43.0ms
(* x (* x x))

simplify3.6s

Counts
35 → 68
Calls
35 calls:
Slowest
482.0ms
(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
474.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
450.0ms
(* (* (* (* x (* x x)) (* x (* x x))) (* x (* x x))) (* (* -2/3 -2/3) -2/3))
338.0ms
(* (exp (* x x)) (exp (* (* x (* x x)) -2/3)))
250.0ms
(* (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x))) (* (* -2/3 -2/3) -2/3))

prune566.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes142.0ms

Accuracy

97.3% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 16.3b

bsearch238.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
3.7s1913×body10240exit
2.7s1743×body1280valid
2.7s10161×body80valid
1.2s1253×body640valid
833.0ms642×body320valid
204.0ms327×body160valid