Details

Time bar (total: 22.6s)

sample67.0ms

Algorithm
intervals
Results
29.0ms283×body80valid
9.0ms106×body80nan

simplify213.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02038
13638
26637
312237
415437
516637
616837
done16837

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize124.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
45.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series522.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
129.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
137.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.0s

Counts
163 → 163
Iterations

Useful iterations: 3 (2.0s)

IterNodesCost
01796238
14174208
211683343
347922690
done50002690

prune729.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize115.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
4.8b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt
10×fma-def
9×times-frac associate-/r*
8×add-log-exp
6×distribute-rgt-neg-in
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out--
3×distribute-lft-neg-in sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l* difference-of-squares
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 98
Calls
4 calls:
48.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
10.0ms
(/ (* a c) b)
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series561.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
273.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
36.0ms
(/ (* a c) b)
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
110 → 110
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01871564
14721463
217351281
done50001212

prune646.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize192.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
37×*-un-lft-identity
34×times-frac
30×add-exp-log
25×add-cube-cbrt
23×add-cbrt-cube
22×associate-*r*
11×cbrt-prod
10×fma-def
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×distribute-rgt-neg-in associate-/r* unswap-sqr
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×distribute-lft-neg-in sqrt-prod div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 frac-times associate-+l- neg-mul-1 rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 136
Calls
4 calls:
28.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
58.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series1.1s

Counts
4 → 12
Calls
4 calls:
137.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
97.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
785.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
148 → 148
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02712697
17492559
229202021
done50011786

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize189.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
1.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
37×add-sqr-sqrt
28×*-un-lft-identity times-frac
27×add-cbrt-cube
16×add-cube-cbrt prod-exp cbrt-unprod
14×cbrt-undiv div-exp
13×associate-*r*
10×cbrt-prod fma-def
8×sqrt-prod add-log-exp unswap-sqr
7×pow1 associate-*l*
6×distribute-rgt-neg-in associate-/r*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×distribute-lft-neg-in div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 frac-times associate-+l- neg-mul-1 rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 135
Calls
4 calls:
114.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
49.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))))))
47.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series1.2s

Counts
4 → 12
Calls
4 calls:
206.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
767.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))))))
124.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
147 → 147
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03253691
18883546
233963064
done50012983

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

regimes481.0ms

Accuracy

90.8% (1.3b remaining)

Error of 8.3b against oracle of 7.0b and baseline of 21.5b

bsearch365.0ms

Steps
ItersRangePoint
9
1.7084993271036838e+35
8.915315724770326e+40
1.7754385347718217e+40
8
-4.810799056667626e+157
-8.81647488783933e+153
-1.367002129773412e+154

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
055163
166163
done66163

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.6s8744×body80valid
399.0ms3010×body80nan