Details

Time bar (total: 31.4s)

sample85.0ms

Algorithm
intervals
Results
22.0ms195×body80valid
14.0ms21×body2560valid
10.0ms20×body1280valid
10.0ms256×pre80true
5.0ms9×body640valid
4.0ms10×body320valid
0.0ms1×body160valid

simplify123.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
123.0ms
(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: 13.9b

localize35.0ms

Local error

Found 4 expressions with local error:

13.8b
(sqrt (fma p (* 4 p) (* x x)))
0.8b
(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
5.0ms
(/ 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)

series556.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
277.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
120.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
85.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
73.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify5.5s

Counts
118 → 97
Calls
118 calls:
Slowest
281.0ms
(/ (* (* x x) x) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))))
277.0ms
(* (* (/ x (sqrt (fma p (* 4 p) (* x x)))) (/ x (sqrt (fma p (* 4 p) (* x x))))) (/ x (sqrt (fma p (* 4 p) (* x x)))))
262.0ms
(* (* (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))
212.0ms
(* (* (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)))
132.0ms
(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.5b

localize31.0ms

Local error

Found 4 expressions with local error:

13.8b
(sqrt (fma p (* 4 p) (* x x)))
0.8b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.5b
(log (exp (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
0.0b
(/ x (sqrt (fma p (* 4 p) (* x x))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
7×log-pow
6×pow1 exp-prod associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/l*
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp fma-udef div-inv
Counts
4 → 90
Calls
4 calls:
Slowest
9.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
7.0ms
(log (exp (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
3.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series936.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
488.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
282.0ms
(log (exp (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
85.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
80.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify6.1s

Counts
124 → 102
Calls
124 calls:
Slowest
324.0ms
(log (exp (* (cbrt (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))) (cbrt (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))))
274.0ms
(* (* (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))
236.0ms
(/ (* (* x x) x) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))))
230.0ms
(* (* (log (exp (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))) (log (exp (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))) (log (exp (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))))
206.0ms
(* (* (/ x (sqrt (fma p (* 4 p) (* x x)))) (/ x (sqrt (fma p (* 4 p) (* x x))))) (/ x (sqrt (fma p (* 4 p) (* x x)))))

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

localize43.0ms

Local error

Found 4 expressions with local error:

13.8b
(sqrt (fma p (* 4 p) (* x x)))
13.8b
(sqrt (fma p (* 4 p) (* x x)))
0.8b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.8b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 54
Calls
4 calls:
Slowest
2.0ms
(sqrt (fma p (* 4 p) (* x x)))
2.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(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)

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
116.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
93.0ms
(sqrt (fma p (* 4 p) (* x x)))
86.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify3.3s

Counts
68 → 66
Calls
68 calls:
Slowest
285.0ms
(* (* (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))
244.0ms
(* (* (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))
161.0ms
(* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x))))
153.0ms
(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
135.0ms
(exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.5b

localize71.0ms

Local error

Found 4 expressions with local error:

13.8b
(sqrt (fma p (* 4 p) (* x x)))
13.8b
(sqrt (fma p (* 4 p) (* x x)))
0.9b
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
0.8b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×sqrt-prod
4×expm1-log1p-u log-prod add-cbrt-cube add-exp-log log-pow insert-posit16 log1p-expm1-u add-log-exp
3×exp-prod
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
1×rem-log-exp exp-sum
Counts
4 → 62
Calls
4 calls:
Slowest
2.0ms
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series319.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
94.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
64.0ms
(sqrt (fma p (* 4 p) (* x x)))
61.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify4.7s

Counts
79 → 74
Calls
79 calls:
Slowest
328.0ms
(* (* (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))) (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))) (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
230.0ms
(log (exp (* (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5)))
206.0ms
(* (* (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))
205.0ms
(log (exp (* (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)) (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))))
186.0ms
(sqrt (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.5b

regimes237.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch11.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s796×body2560valid
790.0ms5943×body80valid
474.0ms634×body1280valid
444.0ms8000×pre80true
190.0ms301×body640valid
65.0ms76×body5120valid
51.0ms153×body320valid
22.0ms97×body160valid