Details

Time bar (total: 19.4s)

sample56.0ms

Algorithm
intervals
Results
10.0ms191×body80valid
9.0ms29×body2560valid
7.0ms29×body1280valid
4.0ms22×body640valid
4.0ms80×body80nan
1.0ms4×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify232.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
131.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
41.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
106.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
58.0ms
(- (* b b) (* 4.0 (* a c)))
118.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
169 → 169
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02436690
15874705
217513760
done50003113

prune586.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow b 2) (* 4.0 (* a c)))
2.4b
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.0b
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
22.1b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
60×*-un-lft-identity
40×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
8×fma-neg prod-diff
7×cbrt-undiv div-exp associate-/r*
6×unpow-prod-down associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod unpow2 sqr-pow
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 162
Calls
4 calls:
35.0ms
(- (pow b 2) (* 4.0 (* a c)))
198.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
123.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
36.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series833.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (pow b 2) (* 4.0 (* a c)))
279.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
346.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
130.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.9s

Counts
174 → 174
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02824848
16874314
228373973
done50003960

prune794.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow b 2) (* 4.0 (* a c)))
2.5b
(* (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
8.0b
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
22.1b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite516.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×add-exp-log
46×*-un-lft-identity
40×times-frac
32×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp
14×difference-of-squares
10×sqrt-prod
8×cbrt-undiv fma-neg prod-diff cbrt-unprod
7×pow1 associate-*r* distribute-lft-out--
6×unpow-prod-down associate-/r* add-log-exp
4×expm1-log1p-u rec-exp flip3-- 1-exp associate-/r/ flip-- log1p-expm1-u
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unpow2 unswap-sqr sqr-pow
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 160
Calls
4 calls:
31.0ms
(- (pow b 2) (* 4.0 (* a c)))
345.0ms
(* (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
108.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
23.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series683.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (pow b 2) (* 4.0 (* a c)))
267.0ms
(* (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
256.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
97.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify2.3s

Counts
172 → 172
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02874566
17463970
230533501
done50013488

prune731.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
0.6b
(- (pow b 2) (* 4.0 (* a c)))
11.2b
(/ (* (* 4.0 a) c) (* 2.0 a))
22.1b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×prod-diff
25×add-exp-log *-un-lft-identity add-cbrt-cube
23×add-cube-cbrt
16×sqrt-prod
14×fma-neg
9×prod-exp cbrt-unprod
8×add-log-exp
6×cbrt-undiv unpow-prod-down div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip--
2×sub-neg sqrt-div diff-log unpow2 difference-of-squares sqr-pow
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 115
Calls
4 calls:
108.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
38.0ms
(- (pow b 2) (* 4.0 (* a c)))
60.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))
35.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
67.0ms
(- (pow b 2) (* 4.0 (* a c)))
12.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))
106.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify2.1s

Counts
127 → 127
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02062344
15192002
222671656
done50001582

prune557.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.0b

regimes301.0ms

Accuracy

88.5% (3.0b remaining)

Error of 8.7b against oracle of 5.7b and baseline of 32.0b

bsearch214.0ms

Steps
ItersRangePoint
0
2.0836136179885362e+135
2.1675125417143413e+135
2.1255630798514387e+135
8
-1.5689852653214878e-249
-6.718454253304289e-254
-9.997712787466912e-253
7
-3.4482088762076956e+69
-1.445974953615168e+68
-3.1028950157805323e+69

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04271
15369
done5369

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.3s1100×body2560valid
1.1s5783×body80valid
455.0ms917×body1280valid
378.0ms2888×body80nan
197.0ms433×body640valid
76.0ms117×body5120valid
58.0ms233×body320valid
21.0ms104×body160valid