Details

Time bar (total: 18.8s)

sample111.0ms

Algorithm
intervals
Results
31.0ms39×body2560valid
20.0ms188×body80valid
16.0ms31×body1280valid
9.0ms87×body80nan
5.0ms13×body640valid
2.0ms6×body320valid
2.0ms3×body5120valid
0.0ms1×body160valid

simplify133.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize40.0ms

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))
0.4b
(- (sqrt (fma (* a c) -4 (* b b))) b)
23.1b
(sqrt (fma (* a c) -4 (* b b)))

rewrite55.0ms

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:
30.0ms
(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms
(fma (* a c) -4 (* b b))
19.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
80.0ms
(fma (* a c) -4 (* b b))
123.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
124.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify2.1s

Counts
126 → 126
Iterations
IterNodes
done5008
32698
2773
1335
0156

prune640.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.5b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (fma (* a c) -4 (* b b))) b)
4.5b
(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
11.1b
(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
23.1b
(sqrt (fma (* a c) -4 (* b b)))

rewrite61.0ms

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:
13.0ms
(+ (sqrt (fma (* a c) -4 (* b b))) b)
32.0ms
(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
10.0ms
(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))

series874.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(+ (sqrt (fma (* a c) -4 (* b b))) b)
291.0ms
(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
298.0ms
(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
131.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify1.8s

Counts
178 → 178
Iterations
IterNodes
done5001
21434
1557
0246

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma c (* a -4) (* b b))
0.1b
(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
1.0b
(+ b (sqrt (fma c (* a -4) (* b b))))
23.1b
(sqrt (fma c (* a -4) (* b b)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
6×add-cbrt-cube add-exp-log add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u
3×fma-def sqrt-prod associate-/l*
2×flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp fma-udef div-inv
Counts
4 → 81
Calls
4 calls:
0.0ms
(fma c (* a -4) (* b b))
17.0ms
(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
9.0ms
(+ b (sqrt (fma c (* a -4) (* b b))))
1.0ms
(sqrt (fma c (* a -4) (* b b)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(fma c (* a -4) (* b b))
259.0ms
(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
111.0ms
(+ b (sqrt (fma c (* a -4) (* b b))))
132.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.0s

Counts
93 → 93
Iterations
IterNodes
done5000
32286
2705
1255
0124

prune784.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 8.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.4b
(- (sqrt (fma (* a c) -4 (* b b))) b)
23.1b
(sqrt (fma (* a c) -4 (* b b)))
23.1b
(sqrt (fma (* a c) -4 (* b b)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
14.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
15.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
112.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
105.0ms
(sqrt (fma (* a c) -4 (* b b)))
124.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify2.5s

Counts
128 → 128
Iterations
IterNodes
done5001
42478
3925
2319
1173
086

prune677.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 8.9b

regimes411.0ms

Accuracy

96.9% (0.7b remaining)

Error of 9.0b against oracle of 8.3b and baseline of 29.6b

bsearch320.0ms

Steps
ItersRangePoint
10
6.2301214455520334e+75
1.5034565205168897e+88
7.386841020175994e+78
7
-4.8398086897492375e-295
-7.680997906572533e-297
-2.170460433232697e-296
9
-5.599802959155633e+154
-4.186518194588193e+147
-1.3282248930815427e+154

simplify16.0ms

Iterations
IterNodes
done54
154
042

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s1064×body2560valid
865.0ms5890×body80valid
344.0ms901×body1280valid
244.0ms447×body640valid
242.0ms2854×body80nan
123.0ms95×body5120valid
45.0ms207×body320valid
20.0ms133×body160valid