Details

Time bar (total: 16.8s)

sample131.0ms

Algorithm
intervals
Results
40.0ms199×body80valid
30.0ms27×body2560valid
14.0ms256×pre80true
14.0ms15×body1280valid
4.0ms6×body640valid
3.0ms2×body5120valid
2.0ms5×body160valid
1.0ms2×body320valid

simplify92.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize36.0ms

Local error

Found 4 expressions with local error:

13.3b
(sqrt (+ (* x x) (* p (* 4 p))))
1.1b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.2b
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
0.0b
(+ (* x x) (* p (* 4 p)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×flip3-+ sqrt-div flip-+ insert-posit16
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 82
Calls
4 calls:
Slowest
11.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
11.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
9.0ms
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
8.0ms
(+ (* x x) (* p (* 4 p)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
80.0ms
(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
64.0ms
(+ (* x x) (* p (* 4 p)))
61.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.1s

Counts
94 → 94

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.0b

localize72.0ms

Local error

Found 4 expressions with local error:

13.3b
(sqrt (+ (* x x) (* p (* 4 p))))
2.8b
(+ (* 0.5 (* x (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))) 0.5)
0.2b
(* x (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))
0.2b
(/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×associate-/r* sqrt-div add-log-exp
5×unswap-sqr
4×flip3-+ div-exp prod-exp associate-/r/ flip-+ insert-posit16
3×associate-*l* pow-flip associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative inv-pow
Counts
4 → 126
Calls
4 calls:
Slowest
67.0ms
(+ (* 0.5 (* x (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))) 0.5)
37.0ms
(* x (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
10.0ms
(/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))

series355.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(+ (* 0.5 (* x (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))) 0.5)
92.0ms
(/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))
78.0ms
(* x (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))
75.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.5s

Counts
138 → 138

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.0b

localize48.0ms

Local error

Found 4 expressions with local error:

13.6b
(pow (+ (* x x) (* p (* 4 p))) (- 1/2))
2.8b
(+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5)
0.2b
(* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))
0.0b
(+ (* x x) (* p (* 4 p)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
10×pow-unpow add-exp-log
8×add-log-exp
7×unpow-prod-down associate-*r*
6×add-cbrt-cube
5×pow1
4×insert-posit16
3×distribute-lft-neg-in pow-neg distribute-rgt-neg-in associate-*l* prod-exp unswap-sqr sqr-pow
2×neg-sub0 pow-to-exp +-commutative sum-log flip3-+ pow-exp associate-*r/ flip-+ pow-sub
1×neg-mul-1 pow-pow un-div-inv *-commutative cbrt-unprod
Counts
4 → 80
Calls
4 calls:
Slowest
57.0ms
(* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))
32.0ms
(+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5)
17.0ms
(+ (* x x) (* p (* 4 p)))
14.0ms
(pow (+ (* x x) (* p (* 4 p))) (- 1/2))

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(pow (+ (* x x) (* p (* 4 p))) (- 1/2))
106.0ms
(+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5)
71.0ms
(* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))
52.0ms
(+ (* x x) (* p (* 4 p)))

simplify1.9s

Counts
92 → 92

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

localize51.0ms

Local error

Found 4 expressions with local error:

13.6b
(pow (+ (* x x) (* p (* 4 p))) (- 1/2))
2.8b
(+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5)
0.5b
(log (+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5))
0.2b
(* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×add-exp-log
10×pow-unpow
7×unpow-prod-down associate-*r*
6×pow1 add-cbrt-cube add-log-exp
4×insert-posit16
3×distribute-lft-neg-in log-prod pow-neg distribute-rgt-neg-in associate-*l* prod-exp unswap-sqr sqr-pow
2×neg-sub0 pow-to-exp log-div flip3-+ pow-exp associate-*r/ flip-+ pow-sub
1×+-commutative neg-mul-1 sum-log pow-pow rem-log-exp log-pow un-div-inv *-commutative cbrt-unprod
Counts
4 → 83
Calls
4 calls:
Slowest
52.0ms
(log (+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5))
46.0ms
(+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5)
33.0ms
(* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))
8.0ms
(pow (+ (* x x) (* p (* 4 p))) (- 1/2))

series470.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(log (+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5))
110.0ms
(pow (+ (* x x) (* p (* 4 p))) (- 1/2))
92.0ms
(+ (* 0.5 (* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))) 0.5)
80.0ms
(* x (pow (+ (* x x) (* p (* 4 p))) (- 1/2)))

simplify1.0s

Counts
95 → 95

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

regimes245.0ms

Accuracy

0% (3.8b remaining)

Error of 13.3b against oracle of 9.5b and baseline of 13.3b

bsearch10.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s6047×body80valid
615.0ms743×body2560valid
494.0ms595×body1280valid
310.0ms8000×pre80true
173.0ms309×body640valid
72.0ms159×body320valid
57.0ms62×body5120valid
21.0ms85×body160valid