Details

Time bar (total: 7.3s)

sample48.0ms

Algorithm
intervals
Results
13.0ms36×body2560valid
8.0ms187×body80valid
5.0ms26×body1280valid
3.0ms19×body640valid
3.0ms73×body80nan
1.0ms5×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219
done1219

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
65.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
98.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0438854
11702750
25001735
done5001735

prune375.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
60.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series591.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
180.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
227.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify153.0ms

Counts
244 → 244
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
08295119
137633863
250013860
done50013860

prune693.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
7.8b
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
75×*-un-lft-identity
60×prod-diff
58×add-cube-cbrt
48×add-exp-log
37×sqrt-prod
30×add-cbrt-cube
27×associate-*r*
25×distribute-rgt-neg-in
24×times-frac
21×distribute-lft-neg-in
17×prod-exp
16×div-exp
10×fma-neg
9×cbrt-undiv cbrt-unprod
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 neg-mul-1
6×associate-/l/
4×expm1-log1p-u frac-times flip3-+ associate-*l/ flip-+ log1p-expm1-u
3×rec-exp flip3-- 1-exp associate-*l* flip-- unswap-sqr
2×sqrt-div diff-log associate-*r/ associate-/r/ un-div-inv div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 200
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
40.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
102.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series588.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
175.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
228.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Counts
212 → 212
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
09144210
150012933
done50012933

prune555.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
8.0b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
61×add-sqr-sqrt
60×*-un-lft-identity prod-diff
54×add-cbrt-cube
48×add-cube-cbrt
40×div-exp
36×sqrt-prod
30×prod-exp
24×distribute-rgt-neg-in
22×cbrt-undiv
21×distribute-lft-neg-in
16×cbrt-unprod
10×fma-neg
8×times-frac 1-exp associate-/l* add-log-exp
7×neg-mul-1
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub associate-*r/ neg-log
Counts
4 → 185
Calls
4 calls:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
76.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
121.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify136.0ms

Counts
197 → 197
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
09544084
145792692
250012690
done50012690

prune410.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes326.0ms

Accuracy

89.6% (2.7b remaining)

Error of 8.2b against oracle of 5.5b and baseline of 31.7b

bsearch471.0ms

Steps
ItersRangePoint
10
1.8478564550364503e-23
1.1395487446675666e-13
3.3294485045805704e-14
9
-3.8269450675186263e-243
-3.0624496234880425e-249
-3.106669992168921e-249
10
-4.9909276054097234e+78
-4.785667473127655e+65
-3.974595954042362e+78

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05030
15230
25230
done5230

end0.0ms

sample1.3s

Algorithm
intervals
Results
268.0ms1107×body2560valid
245.0ms5758×body80valid
175.0ms913×body1280valid
106.0ms2871×body80nan
72.0ms488×body640valid
30.0ms105×body5120valid
25.0ms222×body320valid
8.0ms110×body160valid