Details

Time bar (total: 35.3s)

sample70.0ms

Algorithm
intervals
Results
19.0ms40×body1280valid
15.0ms46×body640valid
9.0ms142×body80valid
4.0ms18×body320valid
1.0ms10×body160valid

simplify5.3s

Counts
1 → 1
Iterations
IterNodes
done5096
83218
7805
6223
597
448
327
220
115
09

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
2.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
13×times-frac
12×add-cube-cbrt
7×add-log-exp
5×add-exp-log add-cbrt-cube distribute-lft-out
4×associate-/r*
3×pow1 associate-/l*
2×flip3-+ associate-/r/ flip-+ difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- div-inv distribute-lft-out--
Counts
3 → 60
Calls
3 calls:
27.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
13.0ms
(+ 1.0 (exp (* -2.0 x)))
139.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series257.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
29.0ms
(+ 1.0 (exp (* -2.0 x)))
159.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.8s

Counts
69 → 69
Iterations
IterNodes
done5004
32165
2717
1261
0116

prune497.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (* (* (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
2.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
30×flip3-- flip--
28×frac-times
26×cbrt-div
19×add-sqr-sqrt
14×associate-*l/
10×*-un-lft-identity add-log-exp
8×associate-*r/
6×difference-of-squares
4×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×sub-neg times-frac diff-log distribute-lft-out--
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 81
Calls
4 calls:
741.0ms
(cbrt (* (* (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
142.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
130.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
145.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series613.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(cbrt (* (* (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
155.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
152.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
155.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify3.3s

Counts
93 → 93
Iterations
IterNodes
done5008
21308
1321
0150

prune676.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize300.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (* (* (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
2.4b
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (* 1.0 1.0)))
2.4b
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (* 1.0 1.0)))
2.4b
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
460×frac-times
458×associate-*r/
324×frac-add
297×flip3-+ flip-+
242×cbrt-div
212×associate-*l/
10×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×sub-neg flip3-- diff-log flip--
2×difference-cubes cube-unmult pow3
1×cbrt-prod pow1/3 difference-of-squares
Counts
4 → 290
Calls
4 calls:
537.0ms
(cbrt (* (* (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
212.0ms
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (* 1.0 1.0)))
209.0ms
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (* 1.0 1.0)))
51.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
659.0ms
(cbrt (* (* (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
249.0ms
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (* 1.0 1.0)))
256.0ms
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 (* 1.0 1.0)))
174.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify6.7s

Counts
302 → 302
Iterations
IterNodes
done5000
13552
0983

prune3.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x 1.0) (* (* x x) (+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17))))
0.0b
(+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17))
0.1b
(* (* x x) (+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17)))
0.9b
(* (* x x) 5.551115123125783e-17)

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
8×add-sqr-sqrt add-log-exp
6×add-cube-cbrt *-un-lft-identity associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in distribute-lft-in flip3-+ associate-*r/ associate-*l* *-commutative flip-+ associate--r+ unswap-sqr
1×+-commutative sub-neg flip3-- diff-log sum-log flip--
Counts
4 → 67
Calls
4 calls:
16.0ms
(- (* x 1.0) (* (* x x) (+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17))))
18.0ms
(+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17))
77.0ms
(* (* x x) (+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17)))
38.0ms
(* (* x x) 5.551115123125783e-17)

series507.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (* x 1.0) (* (* x x) (+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17))))
139.0ms
(+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17))
215.0ms
(* (* x x) (+ (* x 0.33333333333333337) (* (* x x) 5.551115123125783e-17)))
68.0ms
(* (* x x) 5.551115123125783e-17)

simplify3.0s

Counts
79 → 79
Iterations
IterNodes
done5002
21588
1370
0117

prune576.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes521.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.1b

bsearch3.0ms

simplify32.0ms

Iterations
IterNodes
done57
157
039

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.6s1691×body1280valid
470.0ms1210×body640valid
375.0ms4114×body80valid
155.0ms641×body320valid
53.0ms344×body160valid