Details

Time bar (total: 10.2s)

sample277.0ms

Algorithm
intervals
Results
8.0ms181×body80valid
6.0ms27×body2560valid
5.0ms31×body1280valid
3.0ms21×body640valid
3.0ms81×body80nan
2.0ms8×body5120valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify26.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01013
11913
23313
34513
44713
done4713

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

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:
43.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms
(- (* b_2 b_2) (* a c))
74.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify651.0ms

Counts
183 → 183
Iterations

Useful iterations: done (644.0ms)

IterNodesCost
02425993
15364313
214223549
done50003540

prune406.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
2.6b
(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
8.2b
(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
21.1b
(sqrt (- (pow b_2 2) (* a c)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
164×add-sqr-sqrt
162×times-frac
129×*-un-lft-identity
95×add-cube-cbrt
34×difference-of-squares
32×sqrt-prod
27×associate-/l*
18×prod-diff
17×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×fma-neg div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 219
Calls
4 calls:
45.0ms
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
73.0ms
(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
49.0ms
(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
10.0ms
(sqrt (- (pow b_2 2) (* a c)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
100.0ms
(/ (/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
138.0ms
(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
61.0ms
(sqrt (- (pow b_2 2) (* a c)))

simplify1.0s

Counts
231 → 231
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03357469
18026262
223535369
done50005367

prune687.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

5.4b
(exp (log (sqrt (- (pow b_2 2) (* a c)))))
8.6b
(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2))
15.5b
(- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2)
21.1b
(sqrt (- (pow b_2 2) (* a c)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
51×*-un-lft-identity
41×add-cube-cbrt
40×log-prod exp-sum
27×prod-diff
23×sqrt-prod
21×times-frac
15×difference-of-squares
9×fma-neg
7×pow1 associate-/r*
6×add-exp-log exp-prod add-cbrt-cube add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
3×log-pow associate-/l*
2×log-div sqrt-pow1 pow1/2 exp-diff associate-/r/ associate-/l/
1×cbrt-undiv sub-neg rem-sqrt-square frac-2neg flip3-+ diff-log div-exp clear-num flip-+ div-inv rem-exp-log
Counts
4 → 144
Calls
4 calls:
7.0ms
(exp (log (sqrt (- (pow b_2 2) (* a c)))))
61.0ms
(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2))
65.0ms
(- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2)
10.0ms
(sqrt (- (pow b_2 2) (* a c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(exp (log (sqrt (- (pow b_2 2) (* a c)))))
138.0ms
(/ (+ (* b_2 (- b_2 b_2)) (* a c)) (- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2))
76.0ms
(- (exp (log (sqrt (- (pow b_2 2) (* a c))))) b_2)
64.0ms
(sqrt (- (pow b_2 2) (* a c)))

simplify2.2s

Counts
156 → 156
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02353995
14862993
212332410
337952258
done50012254

prune439.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (pow b_2 2) (* a c))
1.2b
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
13.4b
(/ (fma c a 0) (* a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
21.1b
(sqrt (- (pow b_2 2) (* a c)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
27×*-un-lft-identity
26×prod-diff
25×add-cube-cbrt
16×sqrt-prod
14×fma-neg
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×unpow-prod-down
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×times-frac associate-/l*
2×cbrt-undiv sub-neg sqrt-div diff-log associate-*r/ div-exp associate-/r/ unpow2 difference-of-squares sqr-pow
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* cbrt-unprod div-inv distribute-lft-out--
Counts
4 → 113
Calls
4 calls:
9.0ms
(- (pow b_2 2) (* a c))
46.0ms
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
25.0ms
(/ (fma c a 0) (* a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
10.0ms
(sqrt (- (pow b_2 2) (* a c)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (pow b_2 2) (* a c))
75.0ms
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
210.0ms
(/ (fma c a 0) (* a (- (sqrt (- (pow b_2 2) (* a c))) b_2)))
66.0ms
(sqrt (- (pow b_2 2) (* a c)))

simplify736.0ms

Counts
125 → 125
Iterations

Useful iterations: done (728.0ms)

IterNodesCost
02042254
14561952
213541615
done50001592

prune347.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes192.0ms

Accuracy

87.7% (3.3b remaining)

Error of 8.8b against oracle of 5.5b and baseline of 32.0b

bsearch166.0ms

Steps
ItersRangePoint
10
1.1889782913455773e+76
6.845935134449847e+90
2.0945334611922723e+90
9
-2.2089175703627385e-287
-1.7683474342019888e-296
-2.57120366754749e-295
9
-3.339096941797073e+59
-6.124320340976488e+51
-5.109856166749479e+57

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03657
14453
done4453

end0.0ms

sample1.1s

Algorithm
intervals
Results
231.0ms1059×body2560valid
219.0ms5842×body80valid
165.0ms911×body1280valid
108.0ms2942×body80nan
65.0ms463×body640valid
28.0ms103×body5120valid
24.0ms235×body320valid
8.0ms109×body160valid