Details

Time bar (total: 40.2s)

sample39.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
7.0ms256×pre80true

simplify288.0ms

Calls
1 calls:
Slowest
288.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.2b

localize31.0ms

Local error

Found 2 expressions with local error:

13.4b
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
0.3b
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
69×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
44×div-inv
21×associate-/r*
9×add-cbrt-cube add-exp-log
7×associate-/r/ associate-/l*
4×cbrt-undiv div-exp
3×associate-/l/
2×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×flip3-- div-sub flip--
Calls
2 calls:
Slowest
25.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
16.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

series292.0ms

Calls
2 calls:
Slowest
198.0ms
(/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))
93.0ms
(/ (/ i 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

simplify29.7s

Calls
200 calls:
Slowest
829.0ms
(/ (cbrt (/ i 2)) (sqrt (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2))))
615.0ms
(/ (* (* 2 i) (* 2 i)) (/ i 2))
581.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))
470.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (sqrt (/ i 2))))
447.0ms
(/ (/ 1 2) (/ (- (* (* 2 i) (* 2 i)) 1.0) (/ i 2)))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (/ i 2) (- (* 8 i) (/ 2.0 i)))
0.0b
(- (* 8 i) (/ 2.0 i))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×times-frac
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×div-inv
4×add-cbrt-cube add-exp-log associate-/l* add-log-exp
3×associate-/r*
2×pow1 flip3-- associate-/r/ insert-posit16 flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp associate-/l/
Calls
2 calls:
Slowest
6.0ms
(/ (/ i 2) (- (* 8 i) (/ 2.0 i)))
3.0ms
(- (* 8 i) (/ 2.0 i))

series209.0ms

Calls
2 calls:
Slowest
110.0ms
(/ (/ i 2) (- (* 8 i) (/ 2.0 i)))
99.0ms
(- (* 8 i) (/ 2.0 i))

simplify2.5s

Calls
40 calls:
Slowest
538.0ms
(/ (* (* (/ i 2) (/ i 2)) (/ i 2)) (* (* (- (* 8 i) (/ 2.0 i)) (- (* 8 i) (/ 2.0 i))) (- (* 8 i) (/ 2.0 i))))
206.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
190.0ms
(+ (* (* 8 i) (* 8 i)) (+ (* (/ 2.0 i) (/ 2.0 i)) (* (* 8 i) (/ 2.0 i))))
120.0ms
(/ (/ 1 2) (- (* 8 i) (/ 2.0 i)))
114.0ms
(+ (* 0.015625 (/ 1 (pow i 2))) (+ 1/16 (* 0.00390625 (/ 1 (pow i 4)))))

prune330.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

14.1b
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
0.0b
(/ (* i i) 1/4)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×associate-/r* times-frac
2×pow1 clear-num frac-2neg associate-/r/ insert-posit16 div-inv associate-/l* add-log-exp
1×cbrt-undiv flip3-- div-exp flip--
Calls
2 calls:
Slowest
13.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
3.0ms
(/ (* i i) 1/4)

series179.0ms

Calls
2 calls:
Slowest
131.0ms
(/ (* i i) (- (/ (* i i) 1/4) 1.0))
49.0ms
(/ (* i i) 1/4)

simplify1.3s

Calls
19 calls:
Slowest
328.0ms
(+ (* (/ (* i i) 1/4) (/ (* i i) 1/4)) (+ (* 1.0 1.0) (* (/ (* i i) 1/4) 1.0)))
212.0ms
(- (+ (* 1.0 (pow i 2)) (+ (* 4.0 (pow i 4)) (* 16.0 (pow i 6)))))
143.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (- (/ (* i i) 1/4) 1.0) (- (/ (* i i) 1/4) 1.0)) (- (/ (* i i) 1/4) 1.0)))
120.0ms
(+ (* 0.0625 (/ 1 (pow i 2))) (+ 1/4 (* 0.015625 (/ 1 (pow i 4)))))
87.0ms
(+ (* 0.0625 (/ 1 (pow i 2))) (+ 1/4 (* 0.015625 (/ 1 (pow i 4)))))

prune243.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

14.3b
(/ (* i i) (- (log (exp (/ (* i i) 1/4))) 1.0))
0.9b
(log (exp (/ (* i i) 1/4)))
0.0b
(/ (* i i) 1/4)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×add-cbrt-cube add-exp-log log-pow
4×pow1 exp-prod
3×log-prod associate-/r* times-frac insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-/r/ associate-/l*
1×cbrt-undiv flip3-- div-exp rem-log-exp flip--
Calls
3 calls:
Slowest
15.0ms
(/ (* i i) (- (log (exp (/ (* i i) 1/4))) 1.0))
6.0ms
(log (exp (/ (* i i) 1/4)))
5.0ms
(/ (* i i) 1/4)

series154.0ms

Calls
3 calls:
Slowest
93.0ms
(/ (* i i) (- (log (exp (/ (* i i) 1/4))) 1.0))
32.0ms
(/ (* i i) 1/4)
28.0ms
(log (exp (/ (* i i) 1/4)))

simplify1.3s

Calls
30 calls:
Slowest
203.0ms
(- (+ (* 1.0 (pow i 2)) (+ (* 4.0 (pow i 4)) (* 16.0 (pow i 6)))))
200.0ms
(+ (* (log (exp (/ (* i i) 1/4))) (log (exp (/ (* i i) 1/4)))) (+ (* 1.0 1.0) (* (log (exp (/ (* i i) 1/4))) 1.0)))
121.0ms
(+ (* 0.0625 (/ 1 (pow i 2))) (+ 1/4 (* 0.015625 (/ 1 (pow i 4)))))
120.0ms
(+ (* 0.0625 (/ 1 (pow i 2))) (+ 1/4 (* 0.015625 (/ 1 (pow i 4)))))
110.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (- (log (exp (/ (* i i) 1/4))) 1.0) (- (log (exp (/ (* i i) 1/4))) 1.0)) (- (log (exp (/ (* i i) 1/4))) 1.0)))

prune550.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes24.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s8000×body80valid
247.0ms8000×pre80true