Details

Time bar (total: 15.9s)

sample85.0ms

Algorithm
intervals
Results
18.0ms38×body2560valid
15.0ms178×body80valid
11.0ms28×body1280valid
6.0ms79×body80nan
3.0ms11×body640valid
2.0ms3×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify141.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize31.0ms

Local error

Found 4 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)
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite248.0ms

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:
130.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
87.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
111.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms
(- (* b b) (* (* 4.0 a) c))
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
118 → 118
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01952476
14802169
214411861
done50001789

prune587.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 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)
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite203.0ms

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:
80.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
84.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series617.0ms

Counts
4 → 12
Calls
4 calls:
238.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
159.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
85.0ms
(- (* b b) (* (* 4.0 a) c))
134.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
164 → 164
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02614025
15873484
216523082
done50012938

prune601.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite233.0ms

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:
146.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
62.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
100.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
102.0ms
(- (* b b) (* (* 4.0 a) c))
147.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
118 → 118
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01952476
14802169
214411861
done50001789

prune469.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
26×add-exp-log
22×associate-*r*
19×prod-diff sqrt-prod
16×add-cbrt-cube
13×associate-*l*
8×div-exp prod-exp add-log-exp difference-of-squares
7×pow1 fma-neg
6×unswap-sqr
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u distribute-lft-out--
3×flip3-- flip--
2×sub-neg rec-exp sqrt-div diff-log 1-exp div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 141
Calls
4 calls:
122.0ms
(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0))
71.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0))
112.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
62.0ms
(- (* b b) (* (* 4.0 a) c))
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
153 → 153
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02493323
16292903
219412478
done50002409

prune519.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.1b

regimes296.0ms

Accuracy

84.1% (4.6b remaining)

Error of 10.1b against oracle of 5.5b and baseline of 34.3b

bsearch193.0ms

Steps
ItersRangePoint
8
4.924640387312937e-45
5.473977791176249e-42
5.2024432226242543e-45
8
-6.990724105819741e+111
-2.6156774686163576e+108
-1.569310777886352e+111

simplify13.0ms

Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
02942
13838
done3838

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.1s1087×body2560valid
955.0ms5806×body80valid
415.0ms930×body1280valid
318.0ms2994×body80nan
153.0ms446×body640valid
54.0ms117×body5120valid
41.0ms210×body320valid
14.0ms116×body160valid