Details

Time bar (total: 9.3s)

sample41.0ms

Algorithm
intervals
Results
7.0ms34×body2560valid
7.0ms180×body80valid
5.0ms30×body1280valid
3.0ms85×body80nan
2.0ms16×body640valid
0.0ms4×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify74.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
89.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
46.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify973.0ms

Counts
118 → 118
Iterations

Useful iterations: done (969.0ms)

IterNodesCost
01952476
14802169
214411861
done50001789

prune309.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 152
Calls
4 calls:
57.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
52.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify878.0ms

Counts
164 → 164
Iterations

Useful iterations: done (873.0ms)

IterNodesCost
02614025
15873484
216563082
done50012938

prune305.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize3.0ms

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

prune12.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow b 2) (* 4.0 (* a c)))
1.1b
(expm1 (log1p (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (* a 2.0))))
1.4b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
24.3b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×prod-diff
25×*-un-lft-identity
23×add-cube-cbrt
16×sqrt-prod
14×fma-neg
8×add-log-exp
6×unpow-prod-down
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×sub-neg sqrt-div diff-log unpow2 difference-of-squares sqr-pow
1×rem-sqrt-square expm1-log1p sqrt-pow1 pow1/2 distribute-lft-out-- expm1-udef
Counts
4 → 99
Calls
4 calls:
17.0ms
(- (pow b 2) (* 4.0 (* a c)))
0.0ms
(expm1 (log1p (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (* a 2.0))))
80.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
17.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series1.2s

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (pow b 2) (* 4.0 (* a c)))
993.0ms
(expm1 (log1p (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (* a 2.0))))
82.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
72.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify2.6s

Counts
111 → 111
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01812207
14121872
210561598
346851494
done50001494

prune296.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.0b

regimes204.0ms

Accuracy

82.4% (5.0b remaining)

Error of 11.0b against oracle of 6.0b and baseline of 34.6b

bsearch107.0ms

Steps
ItersRangePoint
8
1.7227097696114035e-146
1.4073942755830443e-143
1.3880700472259379e-143
9
-2.0347159842260902e+119
-8.425139364787487e+113
-8.514236331386388e+118

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample1.2s

Algorithm
intervals
Results
237.0ms1092×body2560valid
225.0ms5865×body80valid
170.0ms916×body1280valid
107.0ms2944×body80nan
65.0ms460×body640valid
30.0ms116×body5120valid
22.0ms209×body320valid
7.0ms105×body160valid