Details

Time bar (total: 17.7s)

sample85.0ms

Algorithm
intervals
Results
17.0ms204×body80valid
15.0ms36×body1280valid
12.0ms25×body2560valid
8.0ms104×body80nan
4.0ms15×body640valid
1.0ms5×body320valid
1.0ms1×body5120valid
0.0ms3×body160valid

simplify211.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
312117
415317
516017
616417
done16417

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
123.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
32.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series441.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
136.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
89.0ms
(- (* b b) (* 4.0 (* a c)))
90.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
169 → 169
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02436690
16164729
224663764
done50013675

prune578.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/r*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 156
Calls
4 calls:
67.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
32.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
29.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series561.0ms

Counts
4 → 12
Calls
4 calls:
275.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
121.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
62.0ms
(- (* b b) (* 4.0 (* a c)))
103.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
168 → 168
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02336633
15794664
224873706
done50003619

prune465.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
136.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
38.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series382.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
93.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(- (* b b) (* 4.0 (* a c)))
94.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
177 → 177
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02696947
16904918
230473859
done50013766

prune560.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0))))) (/ 1 (* 2.0 a)))
0.6b
(- (- b) (sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0)))))
7.9b
(* (* a c) (+ (- 4.0) 4.0))
23.9b
(sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0))))

rewrite312.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
65×add-sqr-sqrt
60×prod-diff
54×add-cube-cbrt
35×sqrt-prod
28×add-exp-log
26×distribute-rgt-neg-in
25×distribute-lft-neg-in
20×associate-*r*
18×add-cbrt-cube
13×prod-exp
12×pow1
10×fma-neg
9×neg-mul-1
8×associate-*l* add-log-exp
7×cbrt-unprod
4×expm1-log1p-u distribute-rgt-out div-exp pow-prod-down log1p-expm1-u distribute-lft-out distribute-lft-out-- difference-of-squares
3×flip3-- times-frac associate-*r/ flip--
2×cbrt-undiv frac-times rec-exp distribute-lft1-in flip3-+ sqrt-div diff-log 1-exp associate-*l/ *-commutative flip-+
1×associate--l- neg-sub0 distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 neg-log un-div-inv div-inv unswap-sqr
Counts
4 → 183
Calls
4 calls:
136.0ms
(* (- (- b) (sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0))))) (/ 1 (* 2.0 a)))
55.0ms
(- (- b) (sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0)))))
93.0ms
(* (* a c) (+ (- 4.0) 4.0))
12.0ms
(sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (- (- b) (sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0))))) (/ 1 (* 2.0 a)))
116.0ms
(- (- b) (sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0)))))
5.0ms
(* (* a c) (+ (- 4.0) 4.0))
140.0ms
(sqrt (+ (fma (* 4.0 a) (- c) (* b b)) (* (* a c) (+ (- 4.0) 4.0))))

simplify2.5s

Counts
195 → 195
Iterations

Useful iterations: done (2.5s)

IterNodesCost
030511330
18317855
242155649
done50005648

prune691.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

regimes319.0ms

Accuracy

82.2% (5.2b remaining)

Error of 10.9b against oracle of 5.7b and baseline of 34.9b

bsearch208.0ms

Steps
ItersRangePoint
8
1.051086597250448e+104
1.8086281629461872e+108
7.974731487081542e+107
9
-1.973755526415477e-151
-1.4597075490129595e-159
-1.9334662587143734e-151

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03046
14146
24246
done4246

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.1s1039×body2560valid
943.0ms5893×body80valid
580.0ms929×body1280valid
298.0ms2950×body80nan
198.0ms480×body640valid
54.0ms229×body320valid
51.0ms87×body5120valid
16.0ms109×body160valid