Details

Time bar (total: 22.8s)

sample158.0ms

Algorithm
intervals
Results
16.0ms192×body80valid
13.0ms27×body2560valid
10.0ms105×body80nan
9.0ms23×body1280valid
5.0ms12×body640valid
4.0ms16×body320valid
2.0ms3×body5120valid
1.0ms4×body160valid

simplify119.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
01013
11913
23313
34613
44913
done4913

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize38.0ms

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))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite265.0ms

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:
127.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms
(- (* b_2 b_2) (* a c))
80.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
63.0ms
(- (* b_2 b_2) (* a c))
97.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
114.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
183 → 183
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02425993
15784337
221303551
done50003006

prune805.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
3.3b
(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
9.8b
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
21.2b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite181.0ms

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*
6×flip3-- fma-neg flip-- div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 217
Calls
4 calls:
12.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
94.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
61.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
2.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series737.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
247.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
260.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
108.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.1s

Counts
229 → 229
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03136352
17525415
236265099
done50005039

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
0.8b
(- (pow b_2 2) (* c a))
1.3b
(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
21.2b
(sqrt (- (pow b_2 2) (* c a)))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
174×*-un-lft-identity
165×times-frac
122×add-cube-cbrt
68×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×fma-neg
15×add-exp-log
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×neg-mul-1 flip3-- div-exp flip--
6×pow1 unpow-prod-down
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp unpow2 sqr-pow
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 271
Calls
4 calls:
76.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
20.0ms
(- (pow b_2 2) (* c a))
61.0ms
(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
19.0ms
(sqrt (- (pow b_2 2) (* c a)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
44.0ms
(- (pow b_2 2) (* c a))
91.0ms
(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
68.0ms
(sqrt (- (pow b_2 2) (* c a)))

simplify2.4s

Counts
283 → 283
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03668832
19026686
241795856
done50005855

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b
(- (* b_2 b_2) (* a c))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
63×*-un-lft-identity
61×prod-diff
54×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-exp-log associate-*r*
11×times-frac fma-neg
10×add-log-exp
9×add-cbrt-cube
7×pow1 neg-mul-1 associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg sqrt-div div-exp associate-*l/ cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 169
Calls
4 calls:
141.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
13.0ms
(- (* b_2 b_2) (* a c))
45.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
62.0ms
(- (* b_2 b_2) (* a c))
105.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify5.4s

Counts
181 → 181
Iterations

Useful iterations: done (5.4s)

IterNodesCost
02615917
16454200
235623317
done50003316

prune798.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.1b

regimes441.0ms

Accuracy

85.4% (3.9b remaining)

Error of 9.1b against oracle of 5.2b and baseline of 31.9b

bsearch192.0ms

Steps
ItersRangePoint
9
9.357224410271438e+98
8.450543925883448e+104
5.991199458469861e+103
7
-4.3103989639009063e-82
-2.5085206973204917e-83
-2.534983011264385e-83
3
-1.713609749393423e-29
-1.2239049760790121e-29
-1.6806111715441095e-29

simplify6.0ms

Iterations

Useful iterations: done (5.0ms)

IterNodesCost
04060
14460
done4458

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s5897×body80valid
602.0ms1057×body2560valid
371.0ms855×body1280valid
185.0ms2888×body80nan
120.0ms476×body640valid
113.0ms112×body5120valid
65.0ms117×body160valid
42.0ms218×body320valid