Details

Time bar (total: 15.9s)

sample42.0ms

Algorithm
intervals
Results
13.0ms121×body160valid
7.0ms135×body80valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
02664
18264
224664
376663
4318863
done500063

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize22.0ms

Local error

Found 4 expressions with local error:

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)))))))
0.2b
(* (/ 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))))))))
13.3b
(- 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))))))

rewrite43.0ms

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
pow1 add-log-exp
flip3-+ flip-+
associate-*r*
frac-times associate-*r/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
distribute-rgt-in distribute-lft-in
cbrt-undiv associate-+r+ div-exp pow-prod-down associate-*l/ *-commutative div-inv
+-commutative sub-neg flip3-- diff-log sum-log flip--
Counts
4 → 105
Calls
4 calls:
18.0ms
(* (/ 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)))))))
17.0ms
(* (/ 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)))))
2.0ms
(+ 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))))))))
2.0ms
(- 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))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
303.0ms
(* (/ 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)))))))
201.0ms
(* (/ 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)))))
323.0ms
(+ 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))))))))
854.0ms
(- 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))))))

simplify1.6s

Counts
117 → 117
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02636913
19676532
239935908
done50005907

prune514.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.3b

localize25.0ms

Local error

Found 4 expressions with local error:

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))))))))
0.5b
(cbrt (pow (+ 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)))))))) 3))
0.8b
(pow (+ 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)))))))) 3)
13.3b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (pow (+ 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)))))))) 3))) (exp (- (* (fabs x) (fabs x))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
add-log-exp
unpow-prod-down cube-prod
pow1 add-exp-log add-cbrt-cube
cube-div
pow-unpow flip3-+ flip-+
cube-mult cbrt-div associate-+r+ unpow3 sqr-pow
+-commutative distribute-rgt-in pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in pow1/3 diff-log pow-exp sum-log flip-- rem-cbrt-cube rem-cube-cbrt
Counts
4 → 73
Calls
4 calls:
2.0ms
(+ 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))))))))
3.0ms
(cbrt (pow (+ 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)))))))) 3))
3.0ms
(pow (+ 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)))))))) 3)
2.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (pow (+ 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)))))))) 3))) (exp (- (* (fabs x) (fabs x))))))

series1.9s

Counts
4 → 12
Calls
4 calls:
320.0ms
(+ 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))))))))
315.0ms
(cbrt (pow (+ 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)))))))) 3))
407.0ms
(pow (+ 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)))))))) 3)
851.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (cbrt (pow (+ 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)))))))) 3))) (exp (- (* (fabs x) (fabs x))))))

simplify683.0ms

Counts
85 → 85
Iterations

Useful iterations: done (676.0ms)

IterNodesCost
01596940
14396302
216515473
done50005472

prune354.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (+ (* 0.3275911 (fabs x)) 1.0) 4)
0.2b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
0.4b
(/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
13.3b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (* (fabs x) (fabs x))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
48×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×unpow-prod-down
20×associate-/r*
15×add-exp-log
12×cube-prod
sqr-pow
add-cbrt-cube
div-exp associate-/l* add-log-exp
pow1
cube-mult unpow3 unpow2
pow-to-exp pow-unpow pow-exp
cbrt-undiv cube-div frac-2neg clear-num associate-/r/ div-inv
sub-neg flip3-- pow-pow flip3-+ diff-log flip-- flip-+
Counts
4 → 145
Calls
4 calls:
5.0ms
(pow (+ (* 0.3275911 (fabs x)) 1.0) 4)
14.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
10.0ms
(/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
2.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (* (fabs x) (fabs x))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
52.0ms
(pow (+ (* 0.3275911 (fabs x)) 1.0) 4)
69.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
55.0ms
(/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
862.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (* (fabs x) (fabs x))))))

simplify994.0ms

Counts
157 → 157
Iterations

Useful iterations: done (987.0ms)

IterNodesCost
02754041
15913601
222333324
done50003323

prune661.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
0.4b
(/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
1.2b
(exp (log (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (pow (fabs x) 2)))))))
13.3b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (pow (fabs x) 2)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
48×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
20×associate-/r*
14×add-exp-log
12×cube-prod
add-cbrt-cube sqr-pow
div-exp associate-/l* add-log-exp
pow1
cube-mult exp-prod unpow3 unpow2
log-prod exp-sum
cbrt-undiv cube-div pow-to-exp log-div flip3-- frac-2neg exp-diff pow-exp clear-num associate-/r/ flip-- div-inv
sub-neg flip3-+ diff-log log-pow flip-+ rem-exp-log
Counts
4 → 145
Calls
4 calls:
11.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
10.0ms
(/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
3.0ms
(exp (log (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (pow (fabs x) 2)))))))
2.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (pow (fabs x) 2)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3))
241.0ms
(/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2))
871.0ms
(exp (log (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (pow (fabs x) 2)))))))
871.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (+ (/ 1.421413741 (pow (+ (* 0.3275911 (fabs x)) 1.0) 2)) 0.254829592) (- (/ 1.061405429 (pow (+ (* 0.3275911 (fabs x)) 1.0) 4)) (+ (/ 0.284496736 (+ (* 0.3275911 (fabs x)) 1.0)) (/ 1.453152027 (pow (+ (* 0.3275911 (fabs x)) 1.0) 3)))))) (exp (- (pow (fabs x) 2)))))

simplify792.0ms

Counts
157 → 157
Iterations

Useful iterations: done (785.0ms)

IterNodesCost
02815712
15755230
221954662
done50014660

prune690.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.3b

regimes152.0ms

Accuracy

0% (0.1b remaining)

Error of 13.6b against oracle of 13.5b and baseline of 13.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03664
14464
24664
done4664

end0.0ms

sample769.0ms

Algorithm
intervals
Results
424.0ms3841×body160valid
234.0ms4159×body80valid