Details

Time bar (total: 37.2s)

sample113.0ms

Algorithm
intervals
Results
36.0ms24×body2560valid
28.0ms200×body80valid
13.0ms17×body1280valid
13.0ms256×pre80true
2.0ms5×body320valid
2.0ms2×body5120valid
2.0ms4×body640valid
1.0ms4×body160valid

simplify78.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
77.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize42.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (fma p (* 4 p) (* x x)))
0.9b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0b
(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0b
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
4.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series514.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
258.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
93.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
82.0ms
(sqrt (fma p (* 4 p) (* x x)))
80.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

simplify5.6s

Counts
118 → 97
Calls
118 calls:
Slowest
274.0ms
(/ (* (* x x) x) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))))
254.0ms
(* (* (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)) (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))) (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
237.0ms
(* (* (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5) (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)) (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
218.0ms
(* (* (/ x (sqrt (fma p (* 4 p) (* x x)))) (/ x (sqrt (fma p (* 4 p) (* x x))))) (/ x (sqrt (fma p (* 4 p) (* x x)))))
171.0ms
(* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize28.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (fma p (* 4 p) (* x x)))
4.0b
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
0.2b
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
0.0b
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
22×*-un-lft-identity times-frac associate-*r*
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
5×unswap-sqr
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×rem-sqrt-square sqrt-pow1 pow1/2 div-exp cbrt-unprod
1×cbrt-undiv rec-exp 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
Slowest
11.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
0.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

series541.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
108.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
77.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
66.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify8.6s

Counts
110 → 105
Calls
110 calls:
Slowest
489.0ms
(* (* (* x x) x) (* (* (/ 1 (sqrt (fma p (* 4 p) (* x x)))) (/ 1 (sqrt (fma p (* 4 p) (* x x))))) (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
464.0ms
(* (* (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) (* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))) (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
341.0ms
(* (* (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5) (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)) (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
332.0ms
(* (* (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)) (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))) (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)))
300.0ms
(* (* (* x x) x) (/ (* (* 1 1) 1) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x))))))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.5b

localize24.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (fma x x (* 4 (* p p))))
0.9b
(fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5)
0.0b
(/ x (sqrt (fma x x (* 4 (* p p)))))
0.0b
(sqrt (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
9.0ms
(/ x (sqrt (fma x x (* 4 (* p p)))))
2.0ms
(sqrt (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5))
1.0ms
(sqrt (fma x x (* 4 (* p p))))
0.0ms
(fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5)

series579.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
309.0ms
(sqrt (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5))
122.0ms
(fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5)
75.0ms
(/ x (sqrt (fma x x (* 4 (* p p)))))
72.0ms
(sqrt (fma x x (* 4 (* p p))))

simplify5.5s

Counts
118 → 97
Calls
118 calls:
Slowest
267.0ms
(/ (* (* x x) x) (* (* (sqrt (fma x x (* 4 (* p p)))) (sqrt (fma x x (* 4 (* p p))))) (sqrt (fma x x (* 4 (* p p))))))
244.0ms
(* (* (/ x (sqrt (fma x x (* 4 (* p p))))) (/ x (sqrt (fma x x (* 4 (* p p)))))) (/ x (sqrt (fma x x (* 4 (* p p))))))
216.0ms
(* (* (sqrt (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5)) (sqrt (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5))) (sqrt (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5)))
215.0ms
(* (* (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5) (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5)) (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5))
150.0ms
(exp (fma (/ x (sqrt (fma x x (* 4 (* p p))))) 0.5 0.5))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.5b

localize37.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (fma p (* 4 p) (* x x)))
16.8b
(sqrt (fma p (* 4 p) (* x x)))
6.9b
(fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
0.4b
(/ x (sqrt (sqrt (fma p (* 4 p) (* x x)))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×*-un-lft-identity add-cube-cbrt
27×times-frac
9×associate-/r*
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
Slowest
8.0ms
(/ x (sqrt (sqrt (fma p (* 4 p) (* x x)))))
7.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

series472.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(/ x (sqrt (sqrt (fma p (* 4 p) (* x x)))))
117.0ms
(fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
77.0ms
(sqrt (fma p (* 4 p) (* x x)))
70.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify6.3s

Counts
139 → 109
Calls
139 calls:
Slowest
469.0ms
(/ (* (* x x) x) (* (* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))))
288.0ms
(* (* (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (/ x (sqrt (sqrt (fma p (* 4 p) (* x x)))))) (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))))
247.0ms
(exp (fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
239.0ms
(* (* (fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5) (fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)) (fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
138.0ms
(* (cbrt (fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)) (cbrt (fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.5b

regimes157.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch4.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
824.0ms6081×body80valid
693.0ms313×body640valid
608.0ms742×body2560valid
393.0ms585×body1280valid
355.0ms8000×pre80true
108.0ms145×body320valid
79.0ms60×body5120valid
17.0ms74×body160valid