Details

Time bar (total: 6.4s)

sample46.0ms

Algorithm
intervals
Results
7.0ms173×body80valid
6.0ms29×body2560valid
5.0ms27×body1280valid
4.0msbody5120valid
3.0ms83×body80nan
3.0ms21×body640valid
1.0ms12×body320valid
1.0ms11×body160valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219
done1219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.8b
(- (* b b) (* (* 4.0 a) c))
2.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
add-exp-log add-cbrt-cube
distribute-rgt-neg-in distribute-lft-out
pow1 times-frac associate-/l*
expm1-log1p-u log1p-expm1-u
distribute-lft-neg-in sqrt-prod
cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
68.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
56.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0438854
11702750
25001735
done5001735

prune335.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.1b

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (* b b) (* (* 4.0 a) c))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
associate-/r*
cbrt-undiv div-exp
associate-/r/ add-log-exp
pow1 flip3-- flip--
expm1-log1p-u log1p-expm1-u div-inv
associate-/l/
frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
61.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series529.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 4.0 a) c))
177.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
216.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify130.0ms

Counts
170 → 170
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
06742663
134622412
250012406
done50012406

prune535.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.9b

localize20.0ms

Local error

Found 4 expressions with local error:

6.2b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.1b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
12×times-frac
10×fma-neg prod-diff
add-log-exp
pow1 add-exp-log distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod add-cbrt-cube
difference-of-squares
expm1-log1p-u flip3-- sqrt-div associate-/r* flip-- log1p-expm1-u
associate-/l*
neg-mul-1 rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/ associate-/l/
cbrt-undiv associate--l- neg-sub0 sub-neg frac-2neg flip3-+ div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 108
Calls
4 calls:
16.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
35.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
218.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify97.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
04682299
121451877
250011813
done50011813

prune494.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.9b

localize28.0ms

Local error

Found 4 expressions with local error:

13.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
35×*-un-lft-identity
21×times-frac
19×add-cube-cbrt
13×sqrt-prod
distribute-lft-out-- difference-of-squares
pow1 associate-/r*
add-exp-log sqrt-div add-cbrt-cube
expm1-log1p-u flip3-- distribute-rgt-neg-in flip-- log1p-expm1-u add-log-exp
rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
associate-/r/ associate-/l/
cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
Counts
4 → 100
Calls
4 calls:
60.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
83.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
03631311
118401237
250011228
done50011228

prune500.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.9b

regimes287.0ms

Accuracy

86.6% (3.6b remaining)

Error of 9.1b against oracle of 5.5b and baseline of 32.4b

bsearch153.0ms

Steps
ItersRangePoint
4
9.113314976006761e+77
1.3987841324983815e+78
9.748353205521284e+77
8
-9.073593986373281e-301
-1.0206815961955441e-304
-4.546128927832045e-301
6
-2.609655750368231e+55
-5.8243034561944285e+54
-2.5682011286372237e+55

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04838
15038
25038
done5038

end0.0ms

sample1.2s

Algorithm
intervals
Results
266.0ms1149×body2560valid
226.0ms5800×body80valid
163.0ms887×body1280valid
109.0ms2854×body80nan
73.0ms474×body640valid
27.0ms254×body320valid
25.0ms92×body5120valid
8.0ms108×body160valid