Details

Time bar (total: 14.3s)

sample32.0ms

Algorithm
intervals
Results
13.0ms65×body1280valid
5.0ms40×body640valid
3.0ms126×body80valid
1.0ms11×body320valid
1.0ms14×body160valid

simplify4.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0910
11510
22210
33110
45510
511410
627310
7115810
8406510
done500010

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize7.0ms

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)))
3.9b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite53.0ms

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-exp-log add-cbrt-cube div-inv
4×associate-/r*
3×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- distribute-lft-out--
Counts
3 → 141
Calls
3 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
38.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series135.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
20.0ms
(+ 1.0 (exp (* -2.0 x)))
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify753.0ms

Counts
150 → 150
Iterations

Useful iterations: done (748.0ms)

IterNodesCost
01803092
14082501
212622165
done50012146

prune267.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
6.8b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
1×cube-mult pow-to-exp unpow3 pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 43
Calls
2 calls:
6.0ms
(* 0.33333333333333337 (pow x 3))
0.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series130.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 0.33333333333333337 (pow x 3))
95.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify3.3s

Counts
49 → 49
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
070445
1150409
2554369
33335369
done5001369

prune109.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
3.9b
(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
3.9b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
164×*-un-lft-identity
118×add-sqr-sqrt
108×add-cube-cbrt prod-diff
98×times-frac
59×log-prod
56×exp-sum
26×distribute-lft-out
18×fma-neg
16×associate-/r/
9×flip3-+ flip-+
8×div-inv add-log-exp
7×log-pow
6×add-exp-log exp-prod add-cbrt-cube
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u difference-of-squares
3×fma-def associate-/l*
2×sub-neg distribute-lft-out--
1×cbrt-undiv +-commutative log-div flip3-- frac-2neg exp-diff diff-log div-exp rem-log-exp clear-num sum-log flip--
Counts
4 → 218
Calls
4 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
79.0ms
(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
40.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series205.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
15.0ms
(+ 1.0 (exp (* -2.0 x)))
74.0ms
(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
76.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify650.0ms

Counts
230 → 230
Iterations

Useful iterations: done (642.0ms)

IterNodesCost
03075763
15524359
214753709
done50003685

prune372.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b
(cbrt (+ 1.0 (exp (* -2.0 x))))
31.2b
(fma (/ (sqrt 2.0) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 58
Calls
4 calls:
2.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
3.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
2.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.0ms
(fma (/ (sqrt 2.0) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series838.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
136.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
138.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
439.0ms
(fma (/ (sqrt 2.0) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt 2.0) (cbrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify1.2s

Counts
70 → 70
Iterations

Useful iterations: 3 (260.0ms)

IterNodesCost
0991270
12261215
2713942
33174808
done5001808

prune231.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes319.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03974
14574
done4574

end0.0ms

sample852.0ms

Algorithm
intervals
Results
360.0ms1738×body1280valid
170.0ms1233×body640valid
104.0ms4107×body80valid
56.0ms612×body320valid
18.0ms310×body160valid