Details

Time bar (total: 14.6s)

sample48.0ms

Algorithm
intervals
Results
18.0ms78×body1280valid
11.0ms83×body10240exit
6.0ms47×body640valid
2.0ms95×body80valid
2.0ms24×body320valid
1.0ms12×body160valid

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done8
28
17
05

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.7b
(/ (exp x) (- (exp x) 1.0))
3.6b
(- (exp x) 1.0)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/r* distribute-lft-out-- difference-of-squares
4×add-cbrt-cube add-log-exp
3×add-exp-log associate-/l*
2×pow1 flip3-- associate-/r/ flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
2 → 51
Calls
2 calls:
14.0ms
(/ (exp x) (- (exp x) 1.0))
8.0ms
(- (exp x) 1.0)

series53.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(/ (exp x) (- (exp x) 1.0))
24.0ms
(- (exp x) 1.0)

simplify1.4s

Counts
57 → 57
Iterations
IterNodes
done5000
32908
2645
1191
091

prune259.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×add-sqr-sqrt
4×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×sum-log associate-*r* associate-*l*
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
2 → 31
Calls
2 calls:
47.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
6.0ms
(* 1/12 x)

series54.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
29.0ms
(* 1/12 x)

simplify1.9s

Counts
37 → 37
Iterations
IterNodes
done5001
32896
2524
1156
058

prune169.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp x))
0.6b
(/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x)))))
0.7b
(/ (exp x) (/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x))))))
3.8b
(- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
90×times-frac
58×*-un-lft-identity
56×add-sqr-sqrt add-cube-cbrt
18×associate-/r*
11×add-cbrt-cube associate-/r/
9×add-exp-log
8×add-log-exp
6×flip3-+ flip-+ div-inv associate-/l*
4×pow1 cbrt-undiv div-exp
2×clear-num frac-2neg flip3-- flip-- associate-/l/
1×+-commutative sum-log sub-neg diff-log div-sub distribute-lft-out
Counts
4 → 134
Calls
4 calls:
5.0ms
(+ 1.0 (exp x))
571.0ms
(/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x)))))
350.0ms
(/ (exp x) (/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x))))))
328.0ms
(- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0))

series285.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ 1.0 (exp x))
110.0ms
(/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x)))))
130.0ms
(/ (exp x) (/ (- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x))))))
36.0ms
(- (exp (+ (+ x x) x)) (* (* 1.0 1.0) 1.0))

simplify3.0s

Counts
146 → 146
Iterations
IterNodes
done5000
24858
1759
0264

prune825.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize94.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (exp x) (cbrt (* (* (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0)))) (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0))))) (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0)))))))
3.8b
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))
3.8b
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))
3.8b
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
12×times-frac
9×difference-cubes cube-unmult
7×cbrt-div associate-/r/
5×frac-times add-cbrt-cube associate-*l/ add-exp-log
4×cbrt-prod pow1 associate-/r*
3×exp-lft-cube exp-prod sub-neg flip3-- exp-to-pow diff-log associate-*r/ flip-- associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 83
Calls
4 calls:
8.0ms
(/ (exp x) (cbrt (* (* (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0)))) (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0))))) (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0)))))))
32.0ms
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))
33.0ms
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))
22.0ms
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (exp x) (cbrt (* (* (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0)))) (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0))))) (/ (- (exp (* x 3)) (* 1.0 (* 1.0 1.0))) (+ (* 1.0 1.0) (* (exp x) (+ (exp x) 1.0)))))))
32.0ms
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))
37.0ms
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))
24.0ms
(- (exp (* x 3)) (* 1.0 (* 1.0 1.0)))

simplify1.2s

Counts
95 → 95
Iterations
IterNodes
done5000
21101
1302
0140

prune616.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes54.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 20.6b

bsearch44.0ms

Steps
ItersRangePoint
9
-0.042530208599811804
-3.2052418334402957e-07
-0.0014245372640456257

simplify6.0ms

Iterations
IterNodes
done38
138
027

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.2s2578×body10240exit
666.0ms2275×body1280valid
363.0ms1674×body640valid
133.0ms2759×body80valid
103.0ms857×body320valid
39.0ms435×body160valid