Details

Time bar (total: 15.6s)

sample114.0ms

Algorithm
intervals
Results
30.0ms31×body1280valid
20.0ms35×body2560valid
17.0ms196×body80valid
7.0ms89×body80nan
4.0ms11×body640valid
2.0ms3×body5120valid
0.0ms3×body160valid
0.0ms2×body320valid

simplify138.0ms

Counts
1 → 1
Iterations
IterNodes
done156
6156
5152
4142
3115
264
128
014

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
0.2b
(- (* b b) (* a (* 4.0 c)))
0.8b
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
23.0b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×times-frac add-cube-cbrt associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
103.0ms
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
13.0ms
(- (* b b) (* a (* 4.0 c)))
46.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
14.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
87.0ms
(- (* b b) (* a (* 4.0 c)))
120.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
119.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify913.0ms

Counts
89 → 89
Iterations
IterNodes
done5001
21700
1416
0157

prune530.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
0.2b
(- (* b b) (* a (* 4.0 c)))
0.8b
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
23.0b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log cbrt-unprod pow-flip inv-pow
Counts
4 → 125
Calls
4 calls:
61.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
7.0ms
(- (* b b) (* a (* 4.0 c)))
26.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
15.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
85.0ms
(- (* b b) (* a (* 4.0 c)))
142.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
124.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.2s

Counts
137 → 137
Iterations
IterNodes
done5000
22588
1595
0228

prune597.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* a (* 4.0 c)))
0.2b
(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
0.8b
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
23.0b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×frac-times cbrt-undiv rec-exp sub-neg distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
7.0ms
(- (* b b) (* a (* 4.0 c)))
153.0ms
(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
30.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
14.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* b b) (* a (* 4.0 c)))
129.0ms
(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
101.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
103.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.2s

Counts
97 → 97
Iterations
IterNodes
done5001
22439
1491
0183

prune536.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
3.8b
(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
10.6b
(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
23.0b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-cbrt-cube add-exp-log
14×sqrt-prod
11×distribute-lft-out--
7×cbrt-undiv associate-/r* div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×clear-num frac-2neg sqrt-div prod-exp cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 141
Calls
4 calls:
34.0ms
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
123.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
69.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
7.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series762.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
248.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
296.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
106.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.8s

Counts
153 → 153
Iterations
IterNodes
done5001
23716
1649
0251

prune891.0ms

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 5.4b

regimes603.0ms

Accuracy

88.9% (3.2b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 33.9b

bsearch280.0ms

Steps
ItersRangePoint
10
4.0721326822252617e+40
3.6590220876252264e+50
3.628799960716312e+50
9
-1.2594150945566125e-253
-8.579100536702327e-262
-1.0187986635785929e-256
6
-1.278587798556269e+59
-1.7736353873113924e+58
-1.9700105655521088e+58

simplify4.0ms

Iterations
IterNodes
done41
141
035

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.1s1136×body2560valid
615.0ms5797×body80valid
515.0ms448×body640valid
388.0ms2819×body80nan
335.0ms867×body1280valid
98.0ms238×body320valid
60.0ms109×body5120valid
15.0ms103×body160valid