Details

Time bar (total: 16.2s)

sample59.0ms

Algorithm
intervals
Results
11.0ms197×body80valid
9.0ms28×body2560valid
7.0ms31×body1280valid
4.0ms77×body80nan
3.0ms11×body640valid
1.0ms7×body320valid
1.0ms5×body160valid

simplify126.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite189.0ms

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:
117.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
37.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
101.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(- (* b b) (* 4.0 (* a c)))
135.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01651697
14341584
214641361
done50001347

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize39.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.8b
(/ (/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.4b
(/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite282.0ms

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:
19.0ms
(- (* b b) (* 4.0 (* a c)))
142.0ms
(/ (/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
79.0ms
(/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series649.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* 4.0 (* a c)))
205.0ms
(/ (/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
285.0ms
(/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts
170 → 170
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02635076
16544511
228094181
done50004179

prune744.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize32.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.8b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (* c 4.0) a))) (* 2.0 a))
11.7b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (* c 4.0) a))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
122×add-exp-log
76×add-sqr-sqrt
75×*-un-lft-identity
63×div-exp
58×add-cbrt-cube
45×associate-/l*
43×add-cube-cbrt
34×prod-exp
27×cbrt-undiv
16×distribute-lft-out-- difference-of-squares
14×cbrt-unprod
11×sqrt-prod
10×div-inv
8×rec-exp distribute-rgt-neg-in 1-exp
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div clear-num associate-/r* associate-/r/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff
Counts
4 → 195
Calls
4 calls:
10.0ms
(- (* b b) (* 4.0 (* a c)))
166.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (* c 4.0) a))) (* 2.0 a))
132.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (* c 4.0) a))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* 4.0 (* a c)))
164.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (* c 4.0) a))) (* 2.0 a))
164.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (* c 4.0) a))
93.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts
207 → 207
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03976061
110305676
237864608
done50004605

prune571.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) (* c 4.0))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
147×*-un-lft-identity
144×times-frac
107×add-cube-cbrt
85×associate-*l*
61×prod-diff
43×sqrt-prod
39×add-exp-log
31×distribute-rgt-neg-in
25×add-cbrt-cube
21×distribute-lft-neg-in
20×distribute-lft-out-- difference-of-squares
15×prod-exp
12×div-exp
11×fma-neg
10×pow1 add-log-exp
9×cbrt-unprod
7×neg-mul-1
6×cbrt-undiv flip3-- associate-/r/ flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×diff-log pow-prod-down
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* neg-log associate-*l/ *-commutative
Counts
4 → 238
Calls
4 calls:
182.0ms
(* (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) (* c 4.0))
34.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series423.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) (* c 4.0))
83.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(- (* b b) (* 4.0 (* a c)))
97.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.2s

Counts
250 → 250
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03788844
110076761
227095426
done50004783

prune671.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

regimes356.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.7b

bsearch221.0ms

Steps
ItersRangePoint
8
1.4961070689597945e+139
4.5158951869773294e+141
1.0983508973612419e+141
8
-1.4649997057013753e-301
-1.9636081948043714e-305
-8.517290934480198e-304
5
-1.9941030622962047e+109
-5.928196142097795e+108
-1.8572382657132166e+109

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03765
14665
done4665

end0.0ms

sample1.9s

Algorithm
intervals
Results
355.0ms1069×body2560valid
326.0ms5791×body80valid
256.0ms933×body1280valid
159.0ms2974×body80nan
96.0ms442×body640valid
54.0ms122×body5120valid
44.0ms244×body320valid
13.0ms126×body160valid