Details

Time bar (total: 14.1s)

sample60.0ms

Algorithm
intervals
Results
13.0ms43×body2560valid
9.0ms164×body80valid
8.0ms32×body1280valid
4.0ms80×body80nan
3.0ms16×body640valid
3.0ms8×body5120valid
1.0ms7×body320valid
1.0ms6×body160valid

simplify84.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
014365
124365
244325
379325
499325
5107325
done107325

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.2b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)
1.5b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
148×add-sqr-sqrt
113×*-un-lft-identity
79×add-cube-cbrt
34×difference-of-squares
28×associate-/l*
20×sqrt-prod
17×distribute-lft-out--
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×flip3-- div-sub flip-- associate-/l/
2×clear-num frac-2neg sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 179
Calls
4 calls:
80.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
107.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)
46.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
139.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)
134.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
107.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts
191 → 191
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0288104317
171999801
2299499080
done500298960

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune67.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.4b
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
1.5b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
63×add-sqr-sqrt
47×*-un-lft-identity
44×associate-*r*
42×add-cube-cbrt
24×add-exp-log
18×add-cbrt-cube
12×pow1
9×associate-*l*
8×prod-exp
6×div-exp cbrt-unprod add-log-exp
5×sqrt-prod
4×flip3-- pow-prod-down div-inv flip-- difference-of-squares unswap-sqr
3×cbrt-undiv
2×frac-times sqrt-div associate-*l/ *-commutative distribute-lft-out--
1×rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 diff-log 1-exp associate-*r/
Counts
4 → 123
Calls
4 calls:
12.0ms
(* 4.0 (* a c))
188.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
55.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* 4.0 (* a c))
197.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
122.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
105.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
135 → 135
Iterations

Useful iterations: done (1.2s)

IterNodesCost
028054998
179648605
done500147509

prune816.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.4b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 2.0) a))
1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
63×add-sqr-sqrt
47×*-un-lft-identity
46×associate-*r*
42×add-cube-cbrt
24×add-exp-log
18×add-cbrt-cube
12×pow1
8×prod-exp
7×associate-*l*
6×div-exp cbrt-unprod add-log-exp
5×sqrt-prod
4×flip3-- pow-prod-down div-inv flip-- difference-of-squares unswap-sqr
3×cbrt-undiv
2×frac-times sqrt-div associate-*l/ *-commutative distribute-lft-out--
1×rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 diff-log 1-exp associate-*r/
Counts
4 → 123
Calls
4 calls:
13.0ms
(* (* 4.0 a) c)
192.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 2.0) a))
43.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (* 4.0 a) c)
178.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 2.0) a))
128.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
135 → 135
Iterations

Useful iterations: done (1.1s)

IterNodesCost
028355038
181248604
done500047388

prune783.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.6b

regimes383.0ms

Accuracy

87.9% (4.1b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 39.5b

bsearch80.0ms

Steps
ItersRangePoint
2
3.964947473899983e-62
4.720485511979589e-62
4.626043257219638e-62
7
-5.856362438573669e+138
-1.280729871585891e+137
-3.7108875578650606e+138

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
028869
132869
done32869

end0.0ms

sample3.2s

Algorithm
intervals
Results
899.0ms887×body1280valid
661.0ms1094×body2560valid
513.0ms5792×body80valid
328.0ms2874×body80nan
174.0ms467×body640valid
136.0ms243×body320valid
63.0ms108×body5120valid
17.0ms117×body160valid