Details

Time bar (total: 16.2s)

sample75.0ms

Algorithm
intervals
Results
14.0ms27×body2560valid
14.0ms196×body80valid
10.0ms31×body1280valid
6.0ms92×body80nan
4.0ms16×body640valid
3.0ms5×body5120valid
1.0ms3×body320valid
1.0ms4×body160valid

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.9b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite231.0ms

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:
133.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
63.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
143.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
50.0ms
(- (* b b) (* (* 4.0 a) c))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
118 → 118
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01952476
15212183
224921866
done50001798

prune487.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.9b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite207.0ms

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:
73.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
108.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
142.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
65.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
164 → 164
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02614025
16743498
232343147
done50003070

prune466.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize51.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (* b b) (* (* 4.0 a) c))
131.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
78 → 78
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
0711146
11851058
2843952
done5000952

prune487.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
1.2b
(- (* b b) (* (* 4.0 a) c))
5.6b
(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
86×times-frac
71×prod-diff
57×*-un-lft-identity
56×add-sqr-sqrt
53×add-cube-cbrt
33×sqrt-prod
21×div-inv
11×fma-neg
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/ distribute-lft-out--
1×rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 164
Calls
4 calls:
29.0ms
(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
19.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
71.0ms
(- (* b b) (* (* 4.0 a) c))
141.0ms
(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
176 → 176
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02756226
16945352
227884572
done50004252

prune585.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.5b

regimes338.0ms

Accuracy

85.3% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.5b

bsearch119.0ms

Steps
ItersRangePoint
5
6.945766558749631e-52
1.7836275468166073e-51
8.70366778308292e-52
8
-1.5489453231745737e+155
-2.021963087226922e+151
-2.2976245343188767e+152

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02742
13242
done3242

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.0s1069×body2560valid
691.0ms5754×body80valid
409.0ms917×body1280valid
339.0ms2912×body80nan
132.0ms488×body640valid
82.0ms246×body320valid
53.0ms109×body5120valid
12.0ms91×body160valid