Details

Time bar (total: 30.8s)

sample44.0ms

Algorithm
intervals
Results
13.0ms57×body1280valid
7.0ms39×body640valid
7.0ms17×body160valid
5.0ms130×body80valid
1.0ms13×body320valid

simplify9.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0910
12210
25410
319510
done500010

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize8.0ms

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)))
4.3b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite148.0ms

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:
16.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
7.0ms
(+ 1.0 (exp (* -2.0 x)))
111.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series168.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
18.0ms
(+ 1.0 (exp (* -2.0 x)))
96.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify5.1s

Counts
150 → 150
Iterations

Useful iterations: done (5.1s)

IterNodesCost
01803092
119792302
done50022220

prune334.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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)))
0.1b
(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
4.3b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
100×*-un-lft-identity
69×add-sqr-sqrt
64×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
8×add-log-exp
6×add-exp-log flip3-+ add-cbrt-cube flip-+
5×expm1-log1p-u div-inv
4×pow1 associate-/r* log1p-expm1-u
3×fma-def associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative sub-neg log1p-udef flip3-- frac-2neg diff-log log1p-expm1 div-exp clear-num sum-log flip-- distribute-lft-out--
Counts
4 → 152
Calls
4 calls:
16.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms
(+ 1.0 (exp (* -2.0 x)))
1.0ms
(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
108.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series469.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
18.0ms
(+ 1.0 (exp (* -2.0 x)))
263.0ms
(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
144.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify5.8s

Counts
164 → 164
Iterations

Useful iterations: done (5.8s)

IterNodesCost
01973281
120452488
done50002384

prune431.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

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))
7.2b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite53.0ms

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:
24.0ms
(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
26.0ms
(* 0.33333333333333337 (pow x 3))
1.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series268.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
46.0ms
(* 0.33333333333333337 (pow x 3))
143.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify2.9s

Counts
71 → 71
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01121058
11079842
done5001792

prune277.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 x (* 0.08333333333333327 (pow x 4)))
0.0b
(expm1 (- (fma 1.0 x (* 0.08333333333333327 (pow x 4))) (* 0.5 (pow x 2))))
0.1b
(* 0.08333333333333327 (pow x 4))
13.4b
(- (fma 1.0 x (* 0.08333333333333327 (pow x 4))) (* 0.5 (pow x 2)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×add-cbrt-cube add-log-exp
5×log1p-expm1-u
4×pow1 expm1-log1p-u unpow-prod-down
3×fma-neg associate-*l* prod-diff prod-exp unswap-sqr
2×fma-udef sqr-pow
1×pow-to-exp sub-neg expm1-log1p flip3-- diff-log pow-exp associate--l+ *-commutative flip-- cbrt-unprod expm1-udef
Counts
4 → 69
Calls
4 calls:
0.0ms
(fma 1.0 x (* 0.08333333333333327 (pow x 4)))
0.0ms
(expm1 (- (fma 1.0 x (* 0.08333333333333327 (pow x 4))) (* 0.5 (pow x 2))))
12.0ms
(* 0.08333333333333327 (pow x 4))
7.0ms
(- (fma 1.0 x (* 0.08333333333333327 (pow x 4))) (* 0.5 (pow x 2)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(fma 1.0 x (* 0.08333333333333327 (pow x 4)))
109.0ms
(expm1 (- (fma 1.0 x (* 0.08333333333333327 (pow x 4))) (* 0.5 (pow x 2))))
71.0ms
(* 0.08333333333333327 (pow x 4))
73.0ms
(- (fma 1.0 x (* 0.08333333333333327 (pow x 4))) (* 0.5 (pow x 2)))

simplify1.5s

Counts
81 → 81
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01171123
16291054
done5000962

prune343.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes314.0ms

Accuracy

95.8% (1.2b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 29.6b

bsearch4.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02750
13439
done3439

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s1726×body1280valid
466.0ms1263×body640valid
249.0ms4060×body80valid
107.0ms641×body320valid
34.0ms310×body160valid