Details

Time bar (total: 17.7s)

sample100.0ms

Algorithm
intervals
Results
29.0ms179×body80valid
16.0ms35×body2560valid
13.0ms30×body1280valid
6.0ms76×body80nan
5.0ms8×body5120valid
3.0ms9×body640valid
2.0ms10×body320valid
0.0ms2×body160valid

simplify549.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff sqrt-prod
8×add-exp-log add-cbrt-cube
6×times-frac fma-neg associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×expm1-log1p-u flip3-- flip-- log1p-expm1-u distribute-lft-out--
2×cbrt-undiv sqrt-div div-exp associate-/l/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 90
Calls
3 calls:
158.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
114.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts
3 → 9
Calls
3 calls:
174.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
100.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
99 → 99
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01782210
14531916
213211636
done50001564

prune454.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
66×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
30×add-exp-log
22×sqrt-prod
18×prod-diff associate-/r* add-cbrt-cube
14×div-exp difference-of-squares
11×associate-/r/
7×cbrt-undiv flip3-- flip-- distribute-lft-out--
6×pow1 fma-neg div-inv add-log-exp
4×expm1-log1p-u prod-exp log1p-expm1-u associate-/l*
3×rec-exp 1-exp
2×frac-2neg sqrt-div clear-num cbrt-unprod
1×sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 diff-log inv-pow
Counts
4 → 167
Calls
4 calls:
98.0ms
(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
124.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
99.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series726.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
195.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
104.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
122.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
179 → 179
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02654500
16173949
216963478
done50003333

prune561.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ (/ 1 2.0) a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
83×*-un-lft-identity
78×add-cube-cbrt
71×times-frac
54×prod-diff
43×associate-*l*
35×sqrt-prod
20×distribute-rgt-in distribute-lft-in
18×add-exp-log
12×add-cbrt-cube
6×pow1 fma-neg div-exp associate-*r*
5×prod-exp add-log-exp
4×flip3-- flip-- div-inv difference-of-squares unswap-sqr
3×cbrt-undiv expm1-log1p-u sub-neg cbrt-unprod log1p-expm1-u
2×frac-times sqrt-div associate-*r/ distribute-lft-out--
1×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down associate-*l/ *-commutative
Counts
3 → 175
Calls
3 calls:
208.0ms
(* (/ (/ 1 2.0) a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
73.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
32.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series437.0ms

Counts
3 → 9
Calls
3 calls:
207.0ms
(* (/ (/ 1 2.0) a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
146.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
184 → 184
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03065275
17694529
220593735
done50003421

prune644.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
76.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
65.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
144.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
128 → 128
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01132856
12682310
27181948
327111774
done50011674

prune644.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

regimes352.0ms

Accuracy

83.5% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.0b

bsearch186.0ms

Steps
ItersRangePoint
9
2.3136842542622443e-90
1.8034474160827886e-84
3.091361180800597e-86
6
-3.779251410483496e+105
-5.080294099506613e+104
-1.361733299857302e+105

simplify12.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
02843
13643
done3643

end0.0ms

sample3.4s

Algorithm
intervals
Results
866.0ms906×body1280valid
747.0ms5866×body80valid
602.0ms1023×body2560valid
263.0ms2914×body80nan
152.0ms127×body5120valid
137.0ms442×body640valid
52.0ms244×body320valid
15.0ms109×body160valid