Details

Time bar (total: 31.6s)

sample59.0ms

Algorithm
intervals
Results
34.0ms256×body80valid
10.0ms256×pre80true

simplify235.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
235.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

Local error

Found 2 expressions with local error:

14.9b
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
0.0b
(* 4 (* i i))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube add-exp-log
7×pow1 prod-exp cbrt-unprod
4×add-sqr-sqrt cbrt-undiv div-exp
3×*-un-lft-identity associate-*l* pow-prod-down add-cube-cbrt
2×associate-*l/ associate-/r/ insert-posit16 add-log-exp
1×clear-num associate-/r* frac-2neg times-frac flip3-- associate-*r* *-commutative div-inv flip-- associate-/l* unswap-sqr
Counts
2 → 44
Calls
2 calls:
Slowest
32.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
12.0ms
(* 4 (* i i))

series459.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
415.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
44.0ms
(* 4 (* i i))

simplify3.9s

Counts
28 → 50
Calls
28 calls:
Slowest
478.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
424.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
419.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
342.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
330.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))

prune322.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

14.9b
(* (* i i) (/ 1 (* (- (* 4 (* i i)) 1.0) 4)))
0.2b
(/ 1 (* (- (* 4 (* i i)) 1.0) 4))
0.0b
(* 4 (* i i))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
34×add-cbrt-cube
33×prod-exp
16×pow1
15×cbrt-unprod
12×div-exp
10×add-sqr-sqrt associate-*r*
8×*-un-lft-identity add-cube-cbrt
7×pow-prod-down
6×cbrt-undiv rec-exp times-frac 1-exp
4×associate-*l* associate-*l/ associate-/r/
3×insert-posit16 associate-/l* add-log-exp
2×flip3-- *-commutative div-inv pow-flip flip-- unswap-sqr
1×clear-num associate-/r* frac-2neg associate-*r/ un-div-inv inv-pow
Counts
3 → 95
Calls
3 calls:
Slowest
199.0ms
(* (* i i) (/ 1 (* (- (* 4 (* i i)) 1.0) 4)))
70.0ms
(/ 1 (* (- (* 4 (* i i)) 1.0) 4))
18.0ms
(* 4 (* i i))

series203.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
98.0ms
(* (* i i) (/ 1 (* (- (* 4 (* i i)) 1.0) 4)))
71.0ms
(/ 1 (* (- (* 4 (* i i)) 1.0) 4))
35.0ms
(* 4 (* i i))

simplify11.7s

Counts
72 → 104
Calls
72 calls:
Slowest
461.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
427.0ms
(/ (* (* 1 1) 1) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
416.0ms
(* (* (* (* i i) (* i i)) (* i i)) (/ (* (* 1 1) 1) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4))))
414.0ms
(+ (+ (log i) (log i)) (- (log 1) (+ (log (- (* 4 (* i i)) 1.0)) (log 4))))
409.0ms
(* (* (* (* i i) i) (* (* i i) i)) (/ (* (* 1 1) 1) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4))))

prune748.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

14.3b
(/ i (- (* 4 (* i i)) 1.0))
0.1b
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
0.0b
(* 4 (* i i))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×times-frac
26×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube add-exp-log
18×associate-*l*
14×associate-*r*
10×pow1
7×prod-exp cbrt-unprod
5×cbrt-undiv div-exp unswap-sqr
4×pow-prod-down associate-/r/
3×associate-/r* insert-posit16 div-inv associate-/l* add-log-exp
2×flip3-- *-commutative flip--
1×frac-times clear-num frac-2neg associate-*l/ associate-*r/
Counts
3 → 103
Calls
3 calls:
Slowest
87.0ms
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
24.0ms
(/ i (- (* 4 (* i i)) 1.0))
13.0ms
(* 4 (* i i))

series292.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
124.0ms
(/ i (- (* 4 (* i i)) 1.0))
121.0ms
(* (/ i (- (* 4 (* i i)) 1.0)) (/ i 4))
46.0ms
(* 4 (* i i))

simplify7.1s

Counts
92 → 112
Calls
92 calls:
Slowest
608.0ms
(* (* (* (/ i (- (* 4 (* i i)) 1.0)) (/ i (- (* 4 (* i i)) 1.0))) (/ i (- (* 4 (* i i)) 1.0))) (* (* (/ i 4) (/ i 4)) (/ i 4)))
409.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
354.0ms
(+ (* 0.015625 (/ 1 (pow i 5))) (+ (* 0.0625 (/ 1 (pow i 3))) (* 1/4 (/ 1 i))))
349.0ms
(/ i (- (* (* 4 (* i i)) (* 4 (* i i))) (* 1.0 1.0)))
317.0ms
(+ (* 0.015625 (/ 1 (pow i 5))) (+ (* 0.0625 (/ 1 (pow i 3))) (* 1/4 (/ 1 i))))

prune844.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 0.00390625 (* i i))
0.2b
(/ (+ (/ 0.00390625 (* i i)) 0.015625) (* i i))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
12×add-cbrt-cube add-exp-log
10×*-un-lft-identity
7×times-frac associate-/l*
6×add-sqr-sqrt add-cube-cbrt
4×cbrt-undiv div-exp
2×pow1 clear-num associate-/r* frac-2neg prod-exp cbrt-unprod insert-posit16 div-inv distribute-lft-out add-log-exp associate-/l/
1×flip3-+ flip-+
Counts
2 → 48
Calls
2 calls:
Slowest
50.0ms
(/ (+ (/ 0.00390625 (* i i)) 0.015625) (* i i))
6.0ms
(/ 0.00390625 (* i i))

series157.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
119.0ms
(/ (+ (/ 0.00390625 (* i i)) 0.015625) (* i i))
37.0ms
(/ 0.00390625 (* i i))

simplify2.7s

Counts
34 → 54
Calls
34 calls:
Slowest
342.0ms
(/ (* (* 0.00390625 0.00390625) 0.00390625) (* (* (* i i) i) (* (* i i) i)))
340.0ms
(/ (* (* 0.00390625 0.00390625) 0.00390625) (* (* (* i i) (* i i)) (* i i)))
251.0ms
(- (* (/ 0.00390625 (* i i)) (/ 0.00390625 (* i i))) (* 0.015625 0.015625))
238.0ms
(+ (pow (/ 0.00390625 (* i i)) 3) (pow 0.015625 3))
221.0ms
(/ (* (* (+ (/ 0.00390625 (* i i)) 0.015625) (+ (/ 0.00390625 (* i i)) 0.015625)) (+ (/ 0.00390625 (* i i)) 0.015625)) (* (* (* i i) i) (* (* i i) i)))

prune391.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.5b

bsearch74.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
996.0ms8000×body80valid
710.0ms8000×pre80true