Details

Time bar (total: 16.7s)

sample104.0ms

Algorithm
intervals
Results
26.0ms25×body1280valid
17.0ms36×body2560valid
15.0ms189×body80valid
8.0ms104×body80nan
5.0ms16×body640valid
1.0ms6×body320valid
1.0ms2×body5120valid
0.0ms3×body160valid

simplify171.0ms

Counts
1 → 1
Iterations
IterNodes
done139
7139
6137
5132
4127
3106
261
128
014

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
26.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite140.0ms

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:
79.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
124.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(- (* b b) (* 4.0 (* a c)))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts
89 → 89
Iterations
IterNodes
done5001
34961
21246
1402
0155

prune595.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
26.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

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:
63.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
108.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
89 → 89
Iterations
IterNodes
done5000
21288
1407
0157

prune551.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
26.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite225.0ms

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:
172.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
34.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
130.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
60.0ms
(- (* b b) (* 4.0 (* a c)))
91.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
97 → 97
Iterations
IterNodes
done5002
21644
1467
0181

prune462.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
15.9b
(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* a 2.0))
20.3b
(- (* b b) (* b b))
26.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
5×pow1
3×times-frac flip3-- sqrt-prod flip-- associate-/l*
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-+ distribute-rgt-out-- pow1/2 +-inverses div-sub prod-exp associate-+l- cbrt-unprod flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 67
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* a 2.0))
6.0ms
(- (* b b) (* b b))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* a 2.0))
2.0ms
(- (* b b) (* b b))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
79 → 79
Iterations
IterNodes
done5006
2939
1342
0131

prune440.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.5b

regimes385.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.6b

bsearch256.0ms

Steps
ItersRangePoint
6
5.84949006905106e+100
6.027833473435204e+101
3.355858625783055e+101
9
-1.4598085821258646e-291
-1.0697531889019586e-297
-1.0850002786366243e-297
6
-1.7989235910837076e+89
-1.4585470499056154e+88
-1.7633154797394035e+89

simplify13.0ms

Iterations
IterNodes
done46
146
037

end0.0ms

sample3.7s

Algorithm
intervals
Results
987.0ms1065×body2560valid
860.0ms5822×body80valid
589.0ms948×body1280valid
307.0ms2889×body80nan
148.0ms471×body640valid
128.0ms115×body5120valid
78.0ms241×body320valid
16.0ms107×body160valid