Details

Time bar (total: 31.5s)

sample61.0ms

Algorithm
intervals
Results
37.0ms256×body80valid
9.0ms256×pre80true

simplify284.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
283.0ms
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize31.0ms

Local error

Found 3 expressions with local error:

12.9b
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
0.0b
(* 4 (* i i))
0.0b
(- (* 4 (* i i)) 1.0)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
8×pow1
7×prod-exp cbrt-unprod
5×add-sqr-sqrt add-log-exp
4×cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
3×associate-*l* pow-prod-down insert-posit16
2×flip3-- associate-*l/ associate-/r/ flip--
1×clear-num associate-/r* sub-neg frac-2neg times-frac diff-log associate-*r* *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 57
Calls
3 calls:
Slowest
41.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
19.0ms
(- (* 4 (* i i)) 1.0)
16.0ms
(* 4 (* i i))

series263.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
129.0ms
(/ (* i i) (* (- (* 4 (* i i)) 1.0) 4))
85.0ms
(- (* 4 (* i i)) 1.0)
49.0ms
(* 4 (* i i))

simplify5.1s

Counts
32 → 66
Calls
32 calls:
Slowest
563.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
561.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) 4) (* (- (* 4 (* i i)) 1.0) 4)) (* (- (* 4 (* i i)) 1.0) 4)))
486.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
400.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))
363.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* 4 (* i i)) 1.0) (- (* 4 (* i i)) 1.0)) (- (* 4 (* i i)) 1.0)) (* (* 4 4) 4)))

prune494.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

12.9b
(/ (* i i) (* (- (* (* i i) 4) 1.0) 4))
0.0b
(* (* i i) 4)
0.0b
(- (* (* i i) 4) 1.0)

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
8×pow1
7×prod-exp cbrt-unprod
5×add-sqr-sqrt add-log-exp
4×cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
3×associate-*r* pow-prod-down insert-posit16
2×flip3-- associate-*l/ associate-/r/ flip--
1×clear-num associate-/r* sub-neg frac-2neg times-frac diff-log associate-*l* *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 57
Calls
3 calls:
Slowest
36.0ms
(/ (* i i) (* (- (* (* i i) 4) 1.0) 4))
25.0ms
(- (* (* i i) 4) 1.0)
15.0ms
(* (* i i) 4)

series221.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
100.0ms
(/ (* i i) (* (- (* (* i i) 4) 1.0) 4))
89.0ms
(- (* (* i i) 4) 1.0)
32.0ms
(* (* i i) 4)

simplify4.8s

Counts
32 → 66
Calls
32 calls:
Slowest
561.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* (* i i) 4) 1.0) 4) (* (- (* (* i i) 4) 1.0) 4)) (* (- (* (* i i) 4) 1.0) 4)))
487.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* (* i i) 4) 1.0) 4) (* (- (* (* i i) 4) 1.0) 4)) (* (- (* (* i i) 4) 1.0) 4)))
436.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
414.0ms
(/ (* (* (* i i) i) (* (* i i) i)) (* (* (* (- (* (* i i) 4) 1.0) (- (* (* i i) 4) 1.0)) (- (* (* i i) 4) 1.0)) (* (* 4 4) 4)))
373.0ms
(/ (* (* (* i i) (* i i)) (* i i)) (* (* (* (- (* (* i i) 4) 1.0) (- (* (* i i) 4) 1.0)) (- (* (* i i) 4) 1.0)) (* (* 4 4) 4)))

prune528.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

13.0b
(* (* i i) (/ 1 (* (- (* (* i i) 4) 1.0) 4)))
0.2b
(/ 1 (* (- (* (* i i) 4) 1.0) 4))
0.0b
(* (* i i) 4)
0.0b
(- (* (* i i) 4) 1.0)

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
65×add-exp-log
35×add-cbrt-cube
33×prod-exp
17×pow1
15×cbrt-unprod
12×div-exp associate-*r*
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×pow-prod-down
6×cbrt-undiv rec-exp times-frac 1-exp add-log-exp
4×associate-*l/ associate-/r/ insert-posit16
3×flip3-- flip-- associate-/l*
2×associate-*l* *-commutative div-inv pow-flip unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg diff-log associate-*r/ un-div-inv inv-pow
Counts
4 → 108
Calls
4 calls:
Slowest
222.0ms
(* (* i i) (/ 1 (* (- (* (* i i) 4) 1.0) 4)))
58.0ms
(/ 1 (* (- (* (* i i) 4) 1.0) 4))
34.0ms
(- (* (* i i) 4) 1.0)
29.0ms
(* (* i i) 4)

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(* (* i i) (/ 1 (* (- (* (* i i) 4) 1.0) 4)))
92.0ms
(/ 1 (* (- (* (* i i) 4) 1.0) 4))
86.0ms
(- (* (* i i) 4) 1.0)
43.0ms
(* (* i i) 4)

simplify12.6s

Counts
76 → 120
Calls
76 calls:
Slowest
714.0ms
(+ (log (* i i)) (log (/ 1 (* (- (* (* i i) 4) 1.0) 4))))
453.0ms
(+ (+ (log i) (log i)) (- (log 1) (+ (log (- (* (* i i) 4) 1.0)) (log 4))))
452.0ms
(- (+ (* 0.25 (pow i 2)) (+ (* 1.0 (pow i 4)) (* 4.0 (pow i 6)))))
432.0ms
(+ (* (* (* i i) 4) (* (* i i) 4)) (+ (* 1.0 1.0) (* (* (* i i) 4) 1.0)))
415.0ms
(+ (* (* (* i i) 4) (* (* i i) 4)) (+ (* 1.0 1.0) (* (* (* i i) 4) 1.0)))

prune879.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (+ (/ 0.00390625 (* i i)) 0.015625) (* i i))
0.2b
(/ 0.00390625 (* i i))
0.0b
(+ (/ 0.00390625 (* i i)) 0.015625)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity add-cbrt-cube add-exp-log
7×add-sqr-sqrt times-frac add-cube-cbrt associate-/l*
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 insert-posit16 distribute-lft-out
2×clear-num associate-/r* frac-2neg flip3-+ prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative sum-log
Counts
3 → 61
Calls
3 calls:
Slowest
62.0ms
(/ (+ (/ 0.00390625 (* i i)) 0.015625) (* i i))
31.0ms
(+ (/ 0.00390625 (* i i)) 0.015625)
12.0ms
(/ 0.00390625 (* i i))

series214.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
116.0ms
(/ (+ (/ 0.00390625 (* i i)) 0.015625) (* i i))
67.0ms
(+ (/ 0.00390625 (* i i)) 0.015625)
30.0ms
(/ 0.00390625 (* i i))

simplify2.9s

Counts
39 → 70
Calls
39 calls:
Slowest
352.0ms
(/ (* (* 0.00390625 0.00390625) 0.00390625) (* (* (* i i) (* i i)) (* i i)))
346.0ms
(/ (* (* 0.00390625 0.00390625) 0.00390625) (* (* (* i i) i) (* (* i i) i)))
295.0ms
(+ (pow (/ 0.00390625 (* i i)) 3) (pow 0.015625 3))
255.0ms
(- (* (/ 0.00390625 (* i i)) (/ 0.00390625 (* i i))) (* 0.015625 0.015625))
234.0ms
(/ (* (* (+ (/ 0.00390625 (* i i)) 0.015625) (+ (/ 0.00390625 (* i i)) 0.015625)) (+ (/ 0.00390625 (* i i)) 0.015625)) (* (* (* i i) i) (* (* i i) i)))

prune520.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.7b

bsearch72.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s8000×body80valid
304.0ms8000×pre80true