Details

Time bar (total: 16.2s)

sample57.0ms

Algorithm
intervals
Results
12.0ms178×body80valid
11.0ms41×body2560valid
5.0ms26×body1280valid
3.0ms75×body80nan
2.0ms14×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify31.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01013
11913
23313
34613
44913
done4913

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
118.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms
(- (* b_2 b_2) (* a c))
54.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
43.0ms
(- (* b_2 b_2) (* a c))
105.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
110.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
183 → 183
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02425993
15464313
214083549
done50003001

prune535.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(fma b_2 b_2 (- (* c a)))
3.2b
(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
10.9b
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
24.6b
(sqrt (fma b_2 b_2 (- (* c a))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
6×div-inv
5×pow1 flip3-- flip--
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×associate-/l/
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ fma-udef
Counts
4 → 186
Calls
4 calls:
0.0ms
(fma b_2 b_2 (- (* c a)))
58.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
65.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
3.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

series669.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(fma b_2 b_2 (- (* c a)))
215.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
274.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
109.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.2s

Counts
198 → 198
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02955516
16784787
221104608
done50004543

prune766.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
0.6b
(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
1.0b
(fma b_2 b_2 (- (* c a)))
24.6b
(sqrt (fma b_2 b_2 (- (* c a))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-exp-log fma-neg associate-/r* add-cbrt-cube add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×associate-/l*
2×flip3-- associate-/r/ flip--
1×cbrt-undiv sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-exp clear-num fma-udef div-inv
Counts
4 → 109
Calls
4 calls:
32.0ms
(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
24.0ms
(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
1.0ms
(fma b_2 b_2 (- (* c a)))
3.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

series575.0ms

Counts
4 → 12
Calls
4 calls:
302.0ms
(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
116.0ms
(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
58.0ms
(fma b_2 b_2 (- (* c a)))
99.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.5s

Counts
121 → 121
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01672224
13341950
27021731
319681653
done50001598

prune493.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b
(fma b_2 b_2 (- (* c a)))
15.9b
(fma (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (- b_2))
24.6b
(sqrt (fma b_2 b_2 (- (* c a))))
24.6b
(sqrt (fma b_2 b_2 (- (* c a))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 50
Calls
4 calls:
0.0ms
(fma b_2 b_2 (- (* c a)))
0.0ms
(fma (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (- b_2))
2.0ms
(sqrt (fma b_2 b_2 (- (* c a))))
2.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(fma b_2 b_2 (- (* c a)))
195.0ms
(fma (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (- b_2))
96.0ms
(sqrt (fma b_2 b_2 (- (* c a))))
96.0ms
(sqrt (fma b_2 b_2 (- (* c a))))

simplify3.1s

Counts
62 → 62
Iterations

Useful iterations: 4 (1.5s)

IterNodesCost
062811
1108632
2257570
3833567
42795565
done5001565

prune295.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.3b

regimes238.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.5b

bsearch194.0ms

Steps
ItersRangePoint
9
5.30600492772346e+88
5.894388948599132e+93
3.3616367997262596e+93
10
1.8932238735467414e-306
6.8449465898973125e-295
3.657998399682532e-302
8
-5.7211821970331905e+156
-1.4082798590396656e+153
-1.0772396285489054e+154

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03861
14649
24849
done4849

end0.0ms

sample1.8s

Algorithm
intervals
Results
328.0ms1061×body2560valid
313.0ms5876×body80valid
214.0ms854×body1280valid
150.0ms2976×body80nan
96.0ms471×body640valid
49.0ms113×body5120valid
35.0ms242×body320valid
12.0ms125×body160valid