Details

Time bar (total: 16.1s)

sample80.0ms

Algorithm
intervals
Results
19.0ms45×body1280valid
15.0ms184×body80valid
13.0ms25×body2560valid
6.0ms69×body80nan
5.0ms17×body640valid
2.0ms8×body320valid
2.0ms2×body5120valid
0.0ms2×body160valid

simplify130.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 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:
114.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series474.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
154.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(- (* b b) (* (* 4.0 a) c))
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01671697
14331584
214861361
done50001347

prune402.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.5b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.2b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite245.0ms

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
8×associate-/r*
7×cbrt-undiv div-exp
6×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
1×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))
116.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
100.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series630.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (* b b) (* (* 4.0 a) c))
199.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
261.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
170 → 170
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02625076
16444511
227154181
done50024179

prune739.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize18.0ms

Local error

Found 4 expressions with local error:

9.4b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.4b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
12×times-frac
10×fma-neg prod-diff
8×add-log-exp
6×pow1 add-exp-log distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod add-cbrt-cube
5×difference-of-squares
4×expm1-log1p-u flip3-- sqrt-div associate-/r* flip-- log1p-expm1-u
3×associate-/l*
2×neg-mul-1 rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/ associate-/l/
1×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:
29.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
40.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
31.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series595.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
280.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
120 → 120
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01874229
14462511
215112378
done50012338

prune651.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.2b
(/ (* 2.0 a) (/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.2b
(/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
28×add-sqr-sqrt
27×*-un-lft-identity
20×associate-/r*
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
11×add-cube-cbrt
8×distribute-lft-out-- difference-of-squares
7×sqrt-prod associate-/r/
6×add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u div-inv
2×frac-2neg sqrt-div clear-num associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 124
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
64.0ms
(/ (* 2.0 a) (/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
82.0ms
(/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (* 2.0 a) (/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
242.0ms
(/ (* c (* 4.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
136 → 136
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02393526
16453322
229882738
done50002737

prune655.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.2b

regimes347.0ms

Accuracy

93.9% (1.6b remaining)

Error of 6.9b against oracle of 5.4b and baseline of 31.0b

bsearch332.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
3.2014259215130234e+53
10
-1.2529167750641135e-296
-2.859335985249397e-307
-3.1046203401759487e-300
9
-8.712513212907472e+114
-1.0414090820182828e+108
-2.463372194426505e+111

simplify12.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
03972
14970
done4970

end0.0ms

sample3.6s

Algorithm
intervals
Results
993.0ms1056×body2560valid
850.0ms5848×body80valid
498.0ms922×body1280valid
455.0ms2941×body80nan
167.0ms479×body640valid
74.0ms113×body5120valid
53.0ms208×body320valid
18.0ms109×body160valid