Details

Time bar (total: 32.3s)

sample84.0ms

Algorithm
intervals
Results
37.0ms130×body160valid
19.0ms126×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 3 (574.0ms)

IterNodesCost
02664
18264
229564
3112063
done500263

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
0.2b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))
0.4b
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
14.3b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt associate-*l*
20×add-cube-cbrt *-un-lft-identity times-frac
14×add-exp-log add-cbrt-cube
8×pow1 add-log-exp
6×associate-*r*
5×flip3-+ flip-+
4×prod-exp associate-/r/ cbrt-unprod unswap-sqr
2×cbrt-undiv distribute-rgt-in frac-times associate-+r+ distribute-lft-in associate-*r/ div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×+-commutative sub-neg flip3-- diff-log sum-log flip--
Counts
4 → 99
Calls
4 calls:
46.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
54.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))
14.0ms
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
9.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

series2.2s

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
499.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))
476.0ms
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
1.2s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

simplify2.9s

Counts
111 → 111
Iterations

Useful iterations: 2 (838.0ms)

IterNodesCost
02395553
18095258
247644775
done50014775

prune718.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))
0.6b
(/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
1.0b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
14.3b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (* (fabs x) (fabs x))))))

rewrite800.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
48×*-un-lft-identity
46×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
20×associate-/r*
14×add-exp-log
12×cube-prod
8×add-cbrt-cube add-log-exp sqr-pow
6×div-exp associate-/l*
4×pow1 cube-mult unpow3 unpow2
2×cbrt-undiv cube-div pow-to-exp frac-2neg flip3-+ pow-exp clear-num associate-/r/ flip-+ div-inv
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- distribute-lft-out
Counts
4 → 140
Calls
4 calls:
734.0ms
(+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))
33.0ms
(/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
23.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
5.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (* (fabs x) (fabs x))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
466.0ms
(+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))
84.0ms
(/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
79.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
1.2s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (* (fabs x) (fabs x))))))

simplify2.8s

Counts
152 → 152
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02794791
16674348
243334000
done50003976

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.2b

localize111.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
1.0b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
1.0b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
13.7b
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (pow (fabs x) 2)))) 3))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
65×add-sqr-sqrt
57×*-un-lft-identity
55×add-cube-cbrt
38×unpow-prod-down
24×associate-/r*
19×add-exp-log
18×sqr-pow
12×unpow2
10×add-cbrt-cube
9×div-exp associate-/l*
8×difference-of-squares
6×add-log-exp
4×pow1
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
2×cube-prod
1×difference-cubes sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 169
Calls
4 calls:
47.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
38.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
34.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
29.0ms
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (pow (fabs x) 2)))) 3))

series5.2s

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
72.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
98.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
4.9s
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (pow (fabs x) 2)))) 3))

simplify1.7s

Counts
181 → 181
Iterations

Useful iterations: 2 (626.0ms)

IterNodesCost
02736308
16545869
230065475
done50005475

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.5b

localize182.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
1.0b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
1.0b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
13.8b
(- (pow (sqrt 1.0) 3) (sqrt (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (pow (fabs x) 2)))) 3)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
72×times-frac
57×*-un-lft-identity
55×add-cube-cbrt
42×unpow-prod-down
24×associate-/r*
21×sqr-pow
19×add-exp-log
18×sqrt-prod difference-of-squares
12×unpow2
10×add-cbrt-cube
9×div-exp associate-/l*
6×cube-prod add-log-exp
4×pow1
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 178
Calls
4 calls:
47.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
45.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
30.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
52.0ms
(- (pow (sqrt 1.0) 3) (sqrt (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (pow (fabs x) 2)))) 3)))

series1.7s

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
99.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
71.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
1.4s
(- (pow (sqrt 1.0) 3) (sqrt (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (/ (* (- (+ (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)) (/ 1.421413741 (+ (* 0.3275911 (fabs x)) 1.0))) (+ 0.284496736 (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))) (exp (- (pow (fabs x) 2)))) 3)))

simplify1.2s

Counts
190 → 190
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02147281
14826884
220956424
done50006418

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.4b

regimes394.0ms

Accuracy

0% (0.1b remaining)

Error of 13.2b against oracle of 13.2b and baseline of 13.2b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
051400
166400
done66400

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.7s3973×body160valid
743.0ms4027×body80valid