Details

Time bar (total: 18.9s)

sample99.0ms

Algorithm
intervals
Results
23.0ms30×body1280valid
21.0ms37×body2560valid
18.0ms191×body80valid
9.0ms103×body80nan
6.0ms16×body640valid
2.0ms6×body320valid
1.0ms6×body160valid

simplify104.0ms

Counts
1 → 1
Iterations
IterNodes
done101
7101
6100
598
490
374
244
125
014

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.4b
(fma (* a c) -4 (* b b))
1.6b
(- (sqrt (fma (* a c) -4 (* b b))) b)
21.3b
(sqrt (fma (* a c) -4 (* b b)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
39.0ms
(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms
(fma (* a c) -4 (* b b))
16.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
77.0ms
(fma (* a c) -4 (* b b))
122.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
120.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify1.9s

Counts
126 → 126
Iterations
IterNodes
done5008
32698
2773
1335
0156

prune640.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.9b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (sqrt (fma (* a c) -4 (* b b))) b)
4.1b
(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
10.4b
(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
21.3b
(sqrt (fma (* a c) -4 (* b b)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
101×*-un-lft-identity
68×add-sqr-sqrt
67×add-cube-cbrt
21×associate-/l*
17×distribute-lft-out
11×add-cbrt-cube add-exp-log
10×associate-/r/
7×associate-/r*
6×fma-def flip3-+ sqrt-prod flip-+ div-inv add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u
2×clear-num frac-2neg
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 166
Calls
4 calls:
16.0ms
(+ (sqrt (fma (* a c) -4 (* b b))) b)
51.0ms
(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
35.0ms
(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))

series954.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(+ (sqrt (fma (* a c) -4 (* b b))) b)
351.0ms
(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
344.0ms
(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
125.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify2.0s

Counts
178 → 178
Iterations
IterNodes
done5001
21434
1557
0246

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 1 (* (/ c (+ b (sqrt (fma c (* a -4) (* b b))))) (/ (* a -4) a))) 2)
0.1b
(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
0.6b
(+ b (sqrt (fma c (* a -4) (* b b))))
21.3b
(sqrt (fma c (* a -4) (* b b)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
44×add-cbrt-cube
30×div-exp prod-exp
27×*-un-lft-identity
18×add-sqr-sqrt
17×add-cube-cbrt
16×cbrt-undiv
15×times-frac cbrt-unprod
7×associate-/r* 1-exp
6×add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u associate-/l*
3×fma-def sqrt-prod associate-/l/
2×clear-num frac-2neg flip3-+ associate-/r/ flip-+ div-inv
1×frac-times +-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-*l/
Counts
4 → 116
Calls
4 calls:
127.0ms
(/ (* 1 (* (/ c (+ b (sqrt (fma c (* a -4) (* b b))))) (/ (* a -4) a))) 2)
35.0ms
(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
13.0ms
(+ b (sqrt (fma c (* a -4) (* b b))))
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series690.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(/ (* 1 (* (/ c (+ b (sqrt (fma c (* a -4) (* b b))))) (/ (* a -4) a))) 2)
235.0ms
(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
105.0ms
(+ b (sqrt (fma c (* a -4) (* b b))))
100.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.5s

Counts
128 → 128
Iterations
IterNodes
done5001
22311
1629
0238

prune734.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 1 (* c (/ (* a -4) a))) (* 2 (+ b (sqrt (fma c (* a -4) (* b b))))))
0.6b
(+ b (sqrt (fma c (* a -4) (* b b))))
21.3b
(sqrt (fma c (* a -4) (* b b)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
80×add-exp-log
48×add-cbrt-cube
41×prod-exp
26×div-exp
21×cbrt-unprod
14×cbrt-undiv
8×1-exp
7×*-un-lft-identity
6×add-sqr-sqrt
5×add-cube-cbrt add-log-exp
4×pow1 associate-*r/
3×expm1-log1p-u fma-def sqrt-prod insert-posit16 log1p-expm1-u
2×flip3-+ associate-/r/ flip-+
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log frac-2neg sqrt-pow1 times-frac pow1/2 div-inv distribute-lft-out associate-/l* associate-/l/
Counts
3 → 81
Calls
3 calls:
81.0ms
(/ (* 1 (* c (/ (* a -4) a))) (* 2 (+ b (sqrt (fma c (* a -4) (* b b))))))
7.0ms
(+ b (sqrt (fma c (* a -4) (* b b))))
2.0ms
(sqrt (fma c (* a -4) (* b b)))

series545.0ms

Counts
3 → 9
Calls
3 calls:
311.0ms
(/ (* 1 (* c (/ (* a -4) a))) (* 2 (+ b (sqrt (fma c (* a -4) (* b b))))))
115.0ms
(+ b (sqrt (fma c (* a -4) (* b b))))
118.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.1s

Counts
90 → 90
Iterations
IterNodes
done5001
23467
1551
0186

prune361.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.4b

regimes326.0ms

Accuracy

95.5% (1.0b remaining)

Error of 8.9b against oracle of 7.9b and baseline of 29.1b

bsearch345.0ms

Steps
ItersRangePoint
8
2.5230591910300896e+45
6.095379443414697e+48
5.966643100467746e+48
8
-3.844376447855413e-169
-6.699152817651914e-173
-7.16975135916936e-173
10
-7.277286892276574e+158
-5.475978031765872e+141
-1.374834642760219e+154

simplify9.0ms

Iterations
IterNodes
done58
158
044

end0.0ms

sample3.4s

Algorithm
intervals
Results
939.0ms463×body640valid
657.0ms5918×body80valid
621.0ms1071×body2560valid
345.0ms834×body1280valid
341.0ms3077×body80nan
110.0ms123×body5120valid
56.0ms241×body320valid
18.0ms122×body160valid