Details

Time bar (total: 24.5s)

sample75.0ms

Algorithm
intervals
Results
26.0ms54×body1280valid
14.0ms42×body640valid
8.0ms120×body80valid
5.0ms26×body320valid
2.0ms14×body160valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09234
115234
222234
331234
455234
5122234
6454234
73503234
done5001234

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize14.0ms

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)))
3.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
68×add-sqr-sqrt
63×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
7×add-log-exp
6×flip3-+ flip-+
5×add-cbrt-cube add-exp-log div-inv
4×associate-/r*
3×expm1-log1p-u pow1 fma-def log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log div-exp flip-- distribute-lft-out--
Counts
3 → 141
Calls
3 calls:
11.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
6.0ms
(+ 1.0 (exp (* -2.0 x)))
91.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series173.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
29.0ms
(+ 1.0 (exp (* -2.0 x)))
97.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.4s

Counts
150 → 150
Iterations

Useful iterations: done (1.4s)

IterNodesCost
018063450
142054464
2129445294
done500144087

prune696.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* x x))
0.2b
(* (* x x) 0.33333333333333337)
0.9b
(* 5.551115123125783e-17 (* (* x x) (* x x)))
9.6b
(- (* x (- 1.0 (* (* x x) 0.33333333333333337))) (* 5.551115123125783e-17 (* (* x x) (* x x))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
138×pow1
39×add-cbrt-cube pow-prod-down add-exp-log
36×pow-prod-up
24×prod-exp cbrt-unprod
22×pow-sqr
18×pow-plus
13×pow2
10×add-sqr-sqrt associate--l+
8×*-un-lft-identity add-cube-cbrt
7×prod-diff
6×add-log-exp
5×distribute-rgt-in distribute-lft-in associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×sub-neg *-commutative unswap-sqr
1×flip3-- fma-neg diff-log swap-sqr flip--
Counts
4 → 142
Calls
4 calls:
23.0ms
(* (* x x) (* x x))
21.0ms
(* (* x x) 0.33333333333333337)
91.0ms
(* 5.551115123125783e-17 (* (* x x) (* x x)))
37.0ms
(- (* x (- 1.0 (* (* x x) 0.33333333333333337))) (* 5.551115123125783e-17 (* (* x x) (* x x))))

series232.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* x x) (* x x))
44.0ms
(* (* x x) 0.33333333333333337)
57.0ms
(* 5.551115123125783e-17 (* (* x x) (* x x)))
90.0ms
(- (* x (- 1.0 (* (* x x) 0.33333333333333337))) (* 5.551115123125783e-17 (* (* x x) (* x x))))

simplify3.4s

Counts
154 → 154
Iterations

Useful iterations: done (3.4s)

IterNodesCost
015229218
145623151
2317722436
done500022336

prune478.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.4b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite539.0ms

Algorithm
rewrite-expression-head
Rules
1732×times-frac
1496×*-un-lft-identity
1020×add-sqr-sqrt
997×sqrt-prod
996×add-cube-cbrt
585×prod-diff
249×distribute-lft-out
195×fma-neg
84×sqrt-div associate-/r/
43×flip3-+ flip-+
42×div-inv
30×associate-/l*
14×associate-/r*
11×add-cbrt-cube add-exp-log
8×add-log-exp
7×difference-of-squares
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u
3×fma-def
2×clear-num frac-2neg
1×+-commutative sum-log sub-neg flip3-- diff-log flip-- distribute-lft-out-- associate-/l/
Counts
4 → 1108
Calls
4 calls:
5.0ms
(+ 1.0 (exp (* -2.0 x)))
50.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
14.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
335.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series332.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ 1.0 (exp (* -2.0 x)))
71.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
117.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
114.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify2.6s

Counts
1120 → 1120
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0705748677
11649621867
done5000521175

prune3.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize37.0ms

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))))
3.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite721.0ms

Algorithm
rewrite-expression-head
Rules
232×*-un-lft-identity
169×add-sqr-sqrt
162×prod-diff
154×add-cube-cbrt
147×times-frac
54×fma-neg
36×distribute-lft-out
30×flip3-- flip--
28×frac-times
26×cbrt-div
24×associate-/r/
14×associate-*r/
12×flip3-+ flip-+ div-inv
10×add-log-exp
8×associate-*l/
6×difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×sub-neg diff-log distribute-lft-out--
1×cbrt-prod pow1/3 cube-unmult rem-cbrt-cube
Counts
4 → 305
Calls
4 calls:
395.0ms
(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))))
90.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
115.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
82.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series435.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(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))))
104.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
96.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
119.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.4s

Counts
317 → 317
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0245179653
1511150233
21765119547
done5000116640

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes400.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.2b

bsearch2.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
027938
136938
done36938

end0.0ms

sample1.9s

Algorithm
intervals
Results
650.0ms1764×body1280valid
390.0ms604×body320valid
310.0ms4133×body80valid
295.0ms1180×body640valid
31.0ms319×body160valid