Details

Time bar (total: 38.5s)

sample64.0ms

Algorithm
intervals
Results
30.0ms101×body1280valid
7.0ms26×body640valid
6.0ms108×body80valid
2.0ms13×body320valid
1.0ms8×body160valid

simplify79.0ms

Counts
1 → 1
Iterations
IterNodes
done30
430
328
224
119
09

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
2.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-cbrt-cube add-exp-log
4×insert-posit16
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- pow1/2 diff-log div-exp pow-prod-down sqrt-prod div-inv flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 70
Calls
4 calls:
20.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
16.0ms
(/ 1.0 (hypot 1.0 x))
9.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series487.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
85.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
40.0ms
(/ 1.0 (hypot 1.0 x))
188.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify4.0s

Counts
82 → 82
Iterations
IterNodes
done5003
32016
2676
1242
0116

prune806.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.6b

localize157.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
2.3b
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

rewrite802.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
10×add-cbrt-cube add-exp-log
9×associate-/r* associate-/l*
6×associate-/r/ add-log-exp
5×flip3-+ flip-+
4×pow1 associate-*l/ frac-add associate-*r/ insert-posit16
3×cbrt-undiv clear-num frac-2neg div-exp div-inv
2×flip3-- flip-- associate-/l/
1×sub-neg diff-log div-sub
Counts
4 → 106
Calls
4 calls:
12.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(/ 1.0 (hypot 1.0 x))
592.0ms
(/ (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
172.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

series1.5s

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ 1.0 (hypot 1.0 x))
37.0ms
(/ 1.0 (hypot 1.0 x))
1.1s
(/ (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
379.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

simplify4.9s

Counts
118 → 118
Iterations
IterNodes
done5007
22461
1560
0187

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.6b

localize153.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
2.3b
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
2.3b
(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
20×log-pow
15×exp-prod
10×associate-/l*
9×pow1
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/r/ add-log-exp
5×log-prod flip3-+ flip-+
4×associate-*l/ frac-add associate-*r/ insert-posit16
2×cbrt-undiv log-div clear-num sub-neg frac-2neg exp-diff div-exp exp-sum div-inv
1×flip3-- diff-log div-sub rem-log-exp flip--
Counts
4 → 111
Calls
4 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
1.8s
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
157.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
627.0ms
(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ 1.0 (hypot 1.0 x))
939.0ms
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
363.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
401.0ms
(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))

simplify4.8s

Counts
123 → 123
Iterations
IterNodes
done5002
22241
1578
0232

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.6b

localize214.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (* 1 (/ 1.0 (hypot 1.0 x)))) 0.5))))))
2.3b
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
2.3b
(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
20×log-pow
15×exp-prod
10×associate-/l*
9×pow1
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/r/ add-log-exp
5×log-prod flip3-+ flip-+
4×associate-*l/ frac-add associate-*r/ insert-posit16
2×cbrt-undiv log-div clear-num sub-neg frac-2neg exp-diff div-exp exp-sum div-inv
1×flip3-- diff-log div-sub rem-log-exp flip--
Counts
4 → 111
Calls
4 calls:
9.0ms
(/ 1.0 (hypot 1.0 x))
1.7s
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (* 1 (/ 1.0 (hypot 1.0 x)))) 0.5))))))
170.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
652.0ms
(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 1.0 (hypot 1.0 x))
934.0ms
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (* 1 (/ 1.0 (hypot 1.0 x)))) 0.5))))))
365.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
385.0ms
(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))

simplify4.6s

Counts
123 → 123
Iterations
IterNodes
done5003
22330
1594
0236

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 17.6b

regimes532.0ms

Accuracy

0% (0.0b remaining)

Error of 14.6b against oracle of 14.6b and baseline of 14.6b

bsearch0.0ms

simplify22.0ms

Iterations
IterNodes
done34
134
023

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2850×body1280valid
663.0ms4068×body80valid
155.0ms638×body640valid
50.0ms304×body320valid
15.0ms140×body160valid