Details

Time bar (total: 16.4s)

sample46.0ms

Algorithm
intervals
Results
17.0ms62×body1280valid
6.0ms32×body640valid
5.0ms135×body80valid
2.0ms20×body320valid
1.0ms7×body160valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0910
11510
22210
33110
45510
512210
645410
7340310
done500110

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.5b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite196.0ms

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:
8.0ms
(+ 1.0 (exp (* -2.0 x)))
28.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
153.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series191.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(+ 1.0 (exp (* -2.0 x)))
54.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
119.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify871.0ms

Counts
150 → 150
Iterations

Useful iterations: done (864.0ms)

IterNodesCost
01803092
14192519
212922225
done50002060

prune385.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (+ 1.0 (exp (* -2.0 x))))
0.2b
(sqrt (+ 1.0 (exp (* -2.0 x))))
0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.5b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite743.0ms

Algorithm
rewrite-expression-head
Rules
1375×times-frac
1227×*-un-lft-identity
859×add-sqr-sqrt
829×add-cube-cbrt
797×sqrt-prod
585×prod-diff
198×distribute-lft-out
195×fma-neg
70×sqrt-div
66×associate-/r/
35×flip3-+ flip-+
33×div-inv
7×associate-/r* difference-of-squares
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- distribute-lft-out--
Counts
4 → 887
Calls
4 calls:
14.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
24.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
32.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
519.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series326.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
58.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
98.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
108.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify2.3s

Counts
899 → 899
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
067536223
1156327280
2487323923
done500023923

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.7b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.7b
(cbrt (+ 1.0 (exp (* -2.0 x))))
29.5b
(fma (/ (* (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))))) (fabs (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
22×add-sqr-sqrt add-cube-cbrt
21×times-frac
16×sqrt-prod
8×cbrt-prod
7×associate-/r*
6×add-exp-log add-cbrt-cube distribute-lft-out
4×pow1 expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×flip3-+ flip-+ associate-/l*
2×pow1/3 sqrt-div associate-/r/
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 89
Calls
4 calls:
42.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
11.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
12.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
1.0ms
(fma (/ (* (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))))) (fabs (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
186.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
180.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
641.0ms
(fma (/ (* (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))))) (fabs (cbrt (+ 1.0 (exp (* -2.0 x)))))) (/ (cbrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

simplify601.0ms

Counts
101 → 101
Iterations

Useful iterations: done (597.0ms)

IterNodesCost
01752133
13702014
212571809
done50001790

prune975.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
0.1b
(* 0.33333333333333337 (pow x 3))
7.8b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×associate-*r*
8×add-exp-log add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube add-log-exp
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 expm1-log1p-u associate-*l* prod-diff prod-exp log1p-expm1-u
2×fma-udef sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- fma-neg diff-log unpow3 pow-exp *-commutative flip-- cbrt-unprod associate--r+
Counts
3 → 62
Calls
3 calls:
14.0ms
(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
19.0ms
(* 0.33333333333333337 (pow x 3))
0.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series248.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
42.0ms
(* 0.33333333333333337 (pow x 3))
125.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify1.2s

Counts
71 → 71
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01121058
1285898
21393820
done5000813

prune215.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes365.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.6b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
038102
144102
done44102

end0.0ms

sample1.8s

Algorithm
intervals
Results
528.0ms1629×body1280valid
429.0ms1279×body640valid
337.0ms4116×body80valid
137.0ms647×body320valid
34.0ms329×body160valid