Details

Time bar (total: 20.1s)

sample132.0ms

Algorithm
intervals
Results
45.0ms194×body80valid
29.0ms29×body2560valid
13.0ms256×pre80true
13.0ms17×body1280valid
5.0ms8×body640valid
2.0ms4×body320valid
1.0ms1×body5120valid
1.0ms3×body160valid

simplify122.0ms

Counts
1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize27.0ms

Local error

Found 4 expressions with local error:

16.1b
(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
(fma p (* 4 p) (* x x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×fma-udef
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 80
Calls
4 calls:
Slowest
10.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
3.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma p (* 4 p) (* x x))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series287.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
64.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
60.0ms
(sqrt (fma p (* 4 p) (* x x)))
56.0ms
(fma p (* 4 p) (* x x))

simplify1.1s

Counts
92 → 92

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize42.0ms

Local error

Found 4 expressions with local error:

16.1b
(sqrt (fma p (* 4 p) (* x x)))
0.9b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.4b
(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.1b
(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×log-prod
5×add-exp-log
4×expm1-log1p-u exp-prod add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×exp-sum sqrt-prod
2×log-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp fma-udef rem-exp-log
Counts
4 → 60
Calls
4 calls:
Slowest
9.0ms
(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(log (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)

series539.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
129.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
122.0ms
(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
90.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify2.4s

Counts
72 → 72

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.9b

localize56.0ms

Local error

Found 4 expressions with local error:

16.1b
(sqrt (fma (* p 4) p (* x x)))
0.9b
(log (exp (fma (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5 0.5)))
0.9b
(fma (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5 0.5)
0.0b
(/ x (sqrt (fma (* p 4) p (* x x))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u log-prod log-pow insert-posit16 log1p-expm1-u add-log-exp
3×exp-prod associate-/l*
2×fma-udef
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp exp-sum div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
10.0ms
(/ x (sqrt (fma (* p 4) p (* x x))))
5.0ms
(log (exp (fma (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5 0.5)))
2.0ms
(sqrt (fma (* p 4) p (* x x)))
0.0ms
(fma (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5 0.5)

series358.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(log (exp (fma (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5 0.5)))
102.0ms
(fma (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5 0.5)
72.0ms
(/ x (sqrt (fma (* p 4) p (* x x))))
63.0ms
(sqrt (fma (* p 4) p (* x x)))

simplify4.5s

Counts
100 → 100

prune1.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.9b

localize29.0ms

Local error

Found 4 expressions with local error:

16.1b
(sqrt (fma (* p 4) p (* x x)))
3.1b
(+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5)
0.2b
(* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x)
0.0b
(sqrt (+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
22×associate-*l*
20×*-un-lft-identity times-frac add-cube-cbrt
16×sqrt-prod
9×add-cbrt-cube add-exp-log
8×pow1
6×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* unswap-sqr
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sqrt-div prod-exp cbrt-unprod flip-+
1×cbrt-undiv +-commutative sum-log fma-def div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
21.0ms
(sqrt (+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5))
14.0ms
(* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x)
10.0ms
(+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5)
2.0ms
(sqrt (fma (* p 4) p (* x x)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
222.0ms
(sqrt (+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5))
119.0ms
(* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x)
95.0ms
(+ (* (/ 0.5 (sqrt (fma (* p 4) p (* x x)))) x) 0.5)
63.0ms
(sqrt (fma (* p 4) p (* x x)))

simplify1.1s

Counts
106 → 106

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

regimes191.0ms

Accuracy

0% (1.1b remaining)

Error of 14.0b against oracle of 12.9b and baseline of 14.0b

bsearch6.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s6062×body80valid
646.0ms728×body2560valid
510.0ms613×body1280valid
336.0ms8000×pre80true
208.0ms320×body640valid
49.0ms143×body320valid
46.0ms50×body5120valid
21.0ms84×body160valid