Details

Time bar (total: 13.0s)

sample121.0ms

Algorithm
intervals
Results
33.0ms200×body80valid
26.0ms24×body2560valid
16.0ms17×body1280valid
14.0ms256×pre80true
3.0ms2×body5120valid
3.0ms4×body640valid
3.0ms5×body320valid
1.0ms4×body160valid

simplify91.0ms

Counts
1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize31.0ms

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)

series532.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
262.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
100.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
94.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
76.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.1s

Counts
118 → 97

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize57.0ms

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))

rewrite27.0ms

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
21.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
3.0ms
(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)

series556.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
284.0ms
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
117.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
80.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
75.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify862.0ms

Counts
110 → 105

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize69.0ms

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)))
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)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×fma-udef
Counts
4 → 59
Calls
4 calls:
Slowest
3.0ms
(sqrt (fma p (* 4 p) (* x x)))
2.0ms
(sqrt (fma p (* 4 p) (* x x)))
2.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

series268.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
66.0ms
(sqrt (fma p (* 4 p) (* x x)))
65.0ms
(sqrt (fma p (* 4 p) (* x x)))
52.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify446.0ms

Counts
74 → 71

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.5b

localize46.0ms

Local error

Found 4 expressions with local error:

17.6b
(cbrt (fma p (* 4 p) (* x x)))
17.6b
(cbrt (fma p (* 4 p) (* x x)))
17.6b
(cbrt (fma p (* 4 p) (* x x)))
9.4b
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×cbrt-prod sqrt-pow1 pow1/3
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 64
Calls
4 calls:
Slowest
5.0ms
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
1.0ms
(cbrt (fma p (* 4 p) (* x x)))
1.0ms
(cbrt (fma p (* 4 p) (* x x)))
1.0ms
(cbrt (fma p (* 4 p) (* x x)))

series681.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(cbrt (fma p (* 4 p) (* x x)))
172.0ms
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
160.0ms
(cbrt (fma p (* 4 p) (* x x)))
158.0ms
(cbrt (fma p (* 4 p) (* x x)))

simplify457.0ms

Counts
81 → 76

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.5b

regimes127.0ms

Accuracy

0% (0.9b remaining)

Error of 13.6b against oracle of 12.7b and baseline of 13.6b

bsearch5.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s6081×body80valid
608.0ms742×body2560valid
426.0ms8000×pre80true
381.0ms585×body1280valid
148.0ms313×body640valid
54.0ms60×body5120valid
49.0ms145×body320valid
18.0ms74×body160valid