Details

Time bar (total: 22.0s)

sample70.0ms

Algorithm
intervals
Results
18.0ms203×body80valid
14.0ms256×pre80true
9.0ms16×body2560valid
8.0ms18×body1280valid
4.0ms12×body640valid
1.0ms2×body5120valid
1.0ms3×body160valid
1.0ms2×body320valid

simplify26.0ms

Counts
1 → 1
Iterations
IterNodes
548
448
346
240
128
014

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma p (* 4 p) (* x x))
0.0b
(/ x (sqrt (fma p (* 4 p) (* x x))))
0.3b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
16.4b
(sqrt (fma p (* 4 p) (* x x)))

rewrite9.0ms

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:
0.0ms
(fma p (* 4 p) (* x x))
5.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
2.0ms
(sqrt (fma p (* 4 p) (* x x)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(fma p (* 4 p) (* x x))
87.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
131.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
71.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.4s

Counts
92 → 92
Iterations
IterNodes
43315
3885
2304
1166
0108

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.4b

localize51.0ms

Local error

Found 4 expressions with local error:

2.8b
(/ (fma p (* p 4) (* x x)) x)
4.4b
(/ (* x x) (* (/ (fma p (* p 4) (* x x)) x) (sqrt (fma p (* p 4) (* x x)))))
16.4b
(sqrt (fma p (* p 4) (* x x)))
16.8b
(cbrt (/ (* x x) (* (/ (fma p (* p 4) (* x x)) x) (sqrt (fma p (* p 4) (* x x))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
27×add-cbrt-cube add-exp-log
15×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×times-frac
9×cbrt-undiv div-exp
7×prod-exp cbrt-unprod
6×cbrt-prod
5×pow1
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×sqrt-prod div-inv
2×clear-num frac-2neg associate-*l/ associate-/r/
1×rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 pow1/3
Counts
4 → 93
Calls
4 calls:
5.0ms
(/ (fma p (* p 4) (* x x)) x)
16.0ms
(/ (* x x) (* (/ (fma p (* p 4) (* x x)) x) (sqrt (fma p (* p 4) (* x x)))))
1.0ms
(sqrt (fma p (* p 4) (* x x)))
16.0ms
(cbrt (/ (* x x) (* (/ (fma p (* p 4) (* x x)) x) (sqrt (fma p (* p 4) (* x x))))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (fma p (* p 4) (* x x)) x)
151.0ms
(/ (* x x) (* (/ (fma p (* p 4) (* x x)) x) (sqrt (fma p (* p 4) (* x x)))))
87.0ms
(sqrt (fma p (* p 4) (* x x)))
109.0ms
(cbrt (/ (* x x) (* (/ (fma p (* p 4) (* x x)) x) (sqrt (fma p (* p 4) (* x x))))))

simplify4.1s

Counts
105 → 105
Iterations
IterNodes
36491
21168
1306
0141

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
0.3b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.9b
(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
16.4b
(sqrt (fma p (* 4 p) (* x x)))

rewrite11.0ms

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:
5.0ms
(exp (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)
2.0ms
(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
2.0ms
(sqrt (fma p (* 4 p) (* x x)))

series553.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
112.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
257.0ms
(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
93.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify3.2s

Counts
72 → 72
Iterations
IterNodes
54364
41170
3383
2191
1122
086

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.4b
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
0.9b
(log (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
16.4b
(sqrt (fma p (* 4 p) (* x x)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
11×log-prod
10×add-sqr-sqrt
9×*-un-lft-identity log-pow add-cube-cbrt
8×pow1
6×exp-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×rem-log-exp fma-udef
1×rem-sqrt-square sqrt-pow1 pow1/2 exp-sum
Counts
4 → 65
Calls
4 calls:
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
4.0ms
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
4.0ms
(log (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
3.0ms
(sqrt (fma p (* 4 p) (* x x)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
104.0ms
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
253.0ms
(log (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
96.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.2s

Counts
77 → 77
Iterations
IterNodes
52400
4761
3328
2203
1142
0101

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.4b

regimes191.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
221
121
019

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.1s6049×body80valid
837.0ms8000×pre80true
735.0ms735×body2560valid
395.0ms616×body1280valid
191.0ms302×body640valid
68.0ms165×body320valid
55.0ms58×body5120valid
19.0ms75×body160valid