Details

Time bar (total: 14.6s)

sample132.0ms

Algorithm
intervals
Results
25.0ms43×body2560valid
17.0ms176×body80valid
14.0ms31×body1280valid
10.0ms106×body80nan
7.0ms18×body640valid
3.0ms4×body5120valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
81.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
26.0ms
(- (* b b) (* 4.0 (* a c)))
43.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
69.0ms
(- (* b b) (* 4.0 (* a c)))
114.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
102.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1s

Counts
82 → 82
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01521565
14001461
213151245
348861231
done50001231

prune359.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.1b
(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.7b
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
35.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
116.0ms
(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
138.0ms
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series737.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
237.0ms
(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
273.0ms
(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
166 → 166
Iterations

Useful iterations: 2 (607.0ms)

IterNodesCost
02535113
16224538
224354210
done50004210

prune644.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.8b
(/ (+ (* 4.0 (* a c)) 0) (* (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
7×add-cube-cbrt
5×pow1
4×flip3-- sqrt-prod flip--
3×cbrt-undiv times-frac diff-log div-exp prod-exp cbrt-unprod associate-/l*
2×sub-neg sqrt-div associate-*r/ associate-*l/ associate-/r/ associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 neg-log clear-num associate-/r* flip-+ div-inv
Counts
4 → 72
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
28.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
158.0ms
(/ (+ (* 4.0 (* a c)) 0) (* (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series525.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (* b b) (* 4.0 (* a c)))
142.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
205.0ms
(/ (+ (* 4.0 (* a c)) 0) (* (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0))
102.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts
84 → 84
Iterations

Useful iterations: 2 (539.0ms)

IterNodesCost
01761934
14631717
222631491
done50011491

prune419.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.2b

regimes311.0ms

Accuracy

76.7% (6.1b remaining)

Error of 11.9b against oracle of 5.8b and baseline of 32.1b

bsearch120.0ms

Steps
ItersRangePoint
6
1.6855676195581707e-170
7.565529323099765e-170
7.455592343308264e-170
7
-1.8340745317516165e+50
-1.0728429653156412e+49
-1.5476666036365373e+50

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.4s5876×body80valid
736.0ms1074×body2560valid
397.0ms885×body1280valid
302.0ms3010×body80nan
186.0ms492×body640valid
58.0ms107×body5120valid
45.0ms218×body320valid
13.0ms92×body160valid