Details

Time bar (total: 16.3s)

sample103.0ms

Algorithm
intervals
Results
21.0ms38×body2560valid
18.0ms190×body80valid
16.0ms36×body1280valid
11.0ms79×body80nan
4.0ms11×body640valid
2.0ms4×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify151.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
411916
512816
done12816

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
0.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite214.0ms

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:
134.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
19.0ms
(- (* b b) (* 4.0 (* a c)))
40.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
69.0ms
(- (* b b) (* 4.0 (* a c)))
109.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
103.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01651697
14481588
218601361
done50001352

prune447.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.9b
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
7.7b
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite312.0ms

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:
46.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
146.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
88.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series726.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
237.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
253.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
106.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify656.0ms

Counts
244 → 244
Iterations

Useful iterations: done (638.0ms)

IterNodesCost
033710067
18567629
done50006649

prune909.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.9b
(* (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
7.7b
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
103×*-un-lft-identity
71×add-cube-cbrt
60×prod-diff
51×add-exp-log
46×times-frac
41×sqrt-prod
29×distribute-rgt-neg-in
27×associate-*l* add-cbrt-cube
21×distribute-lft-neg-in
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
10×fma-neg
8×cbrt-undiv cbrt-unprod add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-/r*
4×expm1-log1p-u rec-exp flip3-- 1-exp associate-/r/ flip-- log1p-expm1-u
3×div-inv associate-/l*
2×sqrt-div diff-log associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 227
Calls
4 calls:
56.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
154.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
92.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series868.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
315.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
306.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
103.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify753.0ms

Counts
239 → 239
Iterations

Useful iterations: done (736.0ms)

IterNodesCost
03429661
19627185
done50016075

prune886.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.2b
(- (* b b) (* 4.0 (* a c)))
0.8b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 152
Calls
4 calls:
89.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
10.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series553.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
78.0ms
(- (* b b) (* 4.0 (* a c)))
122.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
116.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.7s

Counts
164 → 164
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02594025
16713498
232533147
done50023070

prune494.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes279.0ms

Accuracy

83.4% (4.5b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 33.0b

bsearch196.0ms

Steps
ItersRangePoint
9
3.58845601849977e-79
3.3299624871078663e-72
4.603517726908401e-74
9
-4.955433086253459e+131
-5.661938264600021e+124
-3.4127765686872833e+126

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample3.4s

Algorithm
intervals
Results
947.0ms5922×body80valid
855.0ms1053×body2560valid
388.0ms906×body1280valid
267.0ms2894×body80nan
180.0ms458×body640valid
82.0ms220×body320valid
48.0ms85×body5120valid
19.0ms121×body160valid