Details

Time bar (total: 17.2s)

sample124.0ms

Algorithm
intervals
Results
39.0ms168×body80valid
18.0ms33×body2560valid
16.0ms35×body1280valid
8.0ms92×body80nan
6.0ms15×body640valid
4.0ms6×body5120valid
3.0ms9×body320valid
1.0ms8×body160valid

simplify139.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite174.0ms

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:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
60.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01671697
14331584
214881361
done50001347

prune468.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.6b
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
19.0ms
(- (* b b) (* (* 4.0 a) c))
144.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
68.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series661.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b b) (* (* 4.0 a) c))
237.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
243.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
170 → 170
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02655076
16544511
228784181
done50004179

prune765.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.9b
(* (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
11.6b
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
58×*-un-lft-identity
51×add-exp-log
46×times-frac
30×add-cube-cbrt
27×associate-*l* add-cbrt-cube
20×prod-exp
16×div-exp
14×distribute-lft-out-- difference-of-squares
10×sqrt-prod
8×cbrt-undiv cbrt-unprod
7×pow1 distribute-rgt-neg-in associate-*r* associate-/r*
6×add-log-exp
4×expm1-log1p-u rec-exp flip3-- 1-exp associate-/r/ flip-- log1p-expm1-u
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 153
Calls
4 calls:
18.0ms
(- (* b b) (* (* 4.0 a) c))
216.0ms
(* (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
67.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series691.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
279.0ms
(* (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
230.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
165 → 165
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02704670
17134061
230723596
done50003594

prune697.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
16.2b
(/ (* c (* 4.0 a)) (* 2.0 a))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 150
Calls
4 calls:
50.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(/ (* c (* 4.0 a)) (* 2.0 a))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (* c (* 4.0 a)) (* 2.0 a))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
162 → 162
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02416254
15944255
224913261
done50003177

prune459.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.2b

regimes383.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.6b

bsearch254.0ms

Steps
ItersRangePoint
5
3.1594096090812424e+104
8.241903478382293e+104
6.2080577970805e+104
8
-4.3193946104502796e-226
-4.381317687258745e-230
-4.487727332912797e-230
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify25.0ms

Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
03766
14664
done4664

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s5870×body80valid
724.0ms1051×body2560valid
384.0ms893×body1280valid
286.0ms2845×body80nan
149.0ms480×body640valid
102.0ms98×body5120valid
48.0ms218×body320valid
17.0ms108×body160valid