Details

Time bar (total: 16.9s)

sample101.0ms

Algorithm
intervals
Results
55.0ms273×body80valid
9.0ms69×body80nan

simplify173.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize162.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4.0 a) c))
90.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
66 → 66
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune472.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize154.0ms

Local error

Found 4 expressions with local error:

7.4b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- flip3-+ neg-log flip-+
Counts
4 → 58
Calls
4 calls:
23.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
131.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
128.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
70 → 70
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0861428
12311014
2776938
32651926
done5000923

prune573.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize140.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.2b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
8.3b
(/ (* a c) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt
8×times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp distribute-lft-out
3×sqrt-prod
2×flip3-- distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 75
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
20.0ms
(/ (* a c) b)
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (* b b) (* (* 4.0 a) c))
259.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
29.0ms
(/ (* a c) b)
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
87 → 87
Iterations

Useful iterations: 2 (308.0ms)

IterNodesCost
01541299
13871235
215071032
done50001032

prune599.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize167.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.2b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* a (/ c b))) b)))
5.2b
(* a (/ c b))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt
15×add-cube-cbrt times-frac
14×add-exp-log add-cbrt-cube
13×associate-*r*
7×pow1
6×add-log-exp
5×associate-/r*
4×distribute-lft-out
3×cbrt-undiv div-exp associate-*l* prod-exp sqrt-prod cbrt-unprod
2×flip3-- distribute-rgt-neg-in sqrt-div associate-/r/ flip-- div-inv unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down clear-num *-commutative flip-+ associate-/l*
Counts
4 → 86
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
182.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* a (/ c b))) b)))
22.0ms
(* a (/ c b))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (* b b) (* (* 4.0 a) c))
290.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* a (/ c b))) b)))
40.0ms
(* a (/ c b))
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
98 → 98
Iterations

Useful iterations: 2 (328.0ms)

IterNodesCost
01781390
14471316
215551113
done50001113

prune509.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

regimes273.0ms

Accuracy

90.7% (1.5b remaining)

Error of 7.8b against oracle of 6.3b and baseline of 22.0b

bsearch502.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
11
-2.859335985249397e-307
9.448397398655464e-278
-5.0660426096144e-310
9
-1.4642911230069481e+159
-8.435593739772907e+149
-1.4341281730542053e+153

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
062190
178154
done78154

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.6s8737×body80valid
382.0ms2941×body80nan