Details

Time bar (total: 15.7s)

sample89.0ms

Algorithm
intervals
Results
17.0ms33×body2560valid
15.0ms181×body80valid
12.0ms27×body1280valid
7.0ms92×body80nan
5.0ms14×body640valid
2.0ms4×body5120valid
2.0ms8×body320valid
1.0ms6×body160valid

simplify88.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01217
12217
24216
38316
411216
512016
done12016

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite256.0ms

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:
137.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
11.0ms
(- (* b b) (* (* 3.0 a) c))
82.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
82.0ms
(- (* b b) (* (* 3.0 a) c))
140.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
86.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.2s

Counts
118 → 118
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01952476
15162185
223791864
done50021796

prune483.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* 3.0 a) (- c) (* b b))
0.2b
(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
1.6b
(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
23.9b
(sqrt (fma (* 3.0 a) (- c) (* b b)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-exp-log add-cbrt-cube
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- 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 fma-udef div-inv
Counts
4 → 98
Calls
4 calls:
0.0ms
(fma (* 3.0 a) (- c) (* b b))
43.0ms
(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
22.0ms
(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
2.0ms
(sqrt (fma (* 3.0 a) (- c) (* b b)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(fma (* 3.0 a) (- c) (* b b))
182.0ms
(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
142.0ms
(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
141.0ms
(sqrt (fma (* 3.0 a) (- c) (* b b)))

simplify870.0ms

Counts
110 → 110
Iterations

Useful iterations: done (865.0ms)

IterNodesCost
01482235
13421961
212521675
done50001595

prune328.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)
3.1b
(/ (/ (fma (- c) (* 3.0 a) 0) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)) (* 3.0 a))
9.5b
(/ (fma (- c) (* 3.0 a) 0) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b))
23.9b
(sqrt (fma (* 3.0 a) (- c) (pow b 2)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity times-frac
33×add-sqr-sqrt
32×add-cube-cbrt
21×associate-/l*
18×add-exp-log add-cbrt-cube
11×distribute-lft-out
7×cbrt-undiv div-exp
6×fma-def sqrt-prod associate-/r/ add-log-exp
5×pow1 associate-/r*
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv
2×frac-2neg prod-exp clear-num cbrt-unprod
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log associate-/l/
Counts
4 → 128
Calls
4 calls:
14.0ms
(+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)
50.0ms
(/ (/ (fma (- c) (* 3.0 a) 0) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)) (* 3.0 a))
16.0ms
(/ (fma (- c) (* 3.0 a) 0) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b))
2.0ms
(sqrt (fma (* 3.0 a) (- c) (pow b 2)))

series803.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)
289.0ms
(/ (/ (fma (- c) (* 3.0 a) 0) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)) (* 3.0 a))
273.0ms
(/ (fma (- c) (* 3.0 a) 0) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b))
106.0ms
(sqrt (fma (* 3.0 a) (- c) (pow b 2)))

simplify1.4s

Counts
140 → 140
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01993696
14823542
221233081
done50023079

prune716.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize41.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)
3.0b
(/ (* a 3.0) (/ (* (- c) (* 3.0 a)) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)))
9.5b
(/ (* (- c) (* 3.0 a)) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b))
23.9b
(sqrt (fma (* 3.0 a) (- c) (pow b 2)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
23×*-un-lft-identity
22×times-frac
17×cbrt-undiv div-exp
14×add-sqr-sqrt associate-/r*
13×add-cube-cbrt prod-exp cbrt-unprod
7×associate-/r/
6×fma-def sqrt-prod add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv
2×frac-2neg clear-num associate-/l*
1×+-commutative distribute-lft-neg-out rem-sqrt-square sqrt-pow1 pow1/2 distribute-frac-neg sum-log
Counts
4 → 115
Calls
4 calls:
14.0ms
(+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)
35.0ms
(/ (* a 3.0) (/ (* (- c) (* 3.0 a)) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)))
43.0ms
(/ (* (- c) (* 3.0 a)) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b))
3.0ms
(sqrt (fma (* 3.0 a) (- c) (pow b 2)))

series675.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)
139.0ms
(/ (* a 3.0) (/ (* (- c) (* 3.0 a)) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b)))
291.0ms
(/ (* (- c) (* 3.0 a)) (+ (sqrt (fma (* 3.0 a) (- c) (pow b 2))) b))
104.0ms
(sqrt (fma (* 3.0 a) (- c) (pow b 2)))

simplify2.4s

Counts
127 → 127
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01953161
15942984
244462450
done50002449

prune596.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

regimes370.0ms

Accuracy

88.9% (3.0b remaining)

Error of 8.5b against oracle of 5.5b and baseline of 32.6b

bsearch188.0ms

Steps
ItersRangePoint
2
2.9557653966214617e-29
3.491579857798755e-29
3.4246030501515935e-29
10
-1.0670407934654806e-296
-4.465562596912786e-307
-3.9602119994834776e-305
9
-1.3908068482385633e+114
-9.803349624800032e+108
-2.063770735185841e+112

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04373
15271
25371
done5371

end0.0ms

sample2.9s

Algorithm
intervals
Results
923.0ms5891×body80valid
563.0ms1092×body2560valid
397.0ms846×body1280valid
249.0ms3046×body80nan
109.0ms465×body640valid
76.0ms96×body5120valid
46.0ms236×body320valid
12.0ms105×body160valid