Details

Time bar (total: 13.9s)

sample89.0ms

Algorithm
intervals
Results
37.0ms271×body80valid
14.0ms102×body80nan

simplify173.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02038
13538
26637
311637
415037
516437
616637
done16637

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize150.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-cbrt-cube sqrt-div add-exp-log
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 63
Calls
4 calls:
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
138.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
128.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify631.0ms

Counts
75 → 75
Iterations

Useful iterations: done (628.0ms)

IterNodesCost
01001330
12541186
210361089
done50001074

prune505.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.8b

localize134.0ms

Local error

Found 4 expressions with local error:

7.1b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1
4×cbrt-div flip3-- add-cbrt-cube add-exp-log flip--
3×sqrt-prod
2×pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log
Counts
4 → 55
Calls
4 calls:
18.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
144.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
143.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify757.0ms

Counts
67 → 67
Iterations

Useful iterations: done (754.0ms)

IterNodesCost
01491566
13741476
215571275
done50011259

prune720.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize184.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-- add-cbrt-cube add-exp-log flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series573.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
169.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
151.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
143.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
66 → 66
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0901170
12111110
27001000
33628985
done5000953

prune712.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.8b

localize164.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.0b
(/ (* a c) b)
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×associate-/r* times-frac
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod
2×clear-num sum-log frac-2neg flip3-- sqrt-div prod-exp associate-/r/ cbrt-unprod div-inv flip-- distribute-lft-out associate-/l*
1×neg-sub0 +-commutative rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log associate-+l- flip-+
Counts
4 → 74
Calls
4 calls:
20.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
7.0ms
(/ (* a c) b)
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
94.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
31.0ms
(/ (* a c) b)
89.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
86 → 86
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01731340
14881252
227151090
done50001086

prune624.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

regimes447.0ms

Accuracy

91.7% (1.1b remaining)

Error of 7.8b against oracle of 6.7b and baseline of 20.1b

bsearch334.0ms

Steps
ItersRangePoint
9
6.258218916731328e+93
1.8883840965187804e+99
2.3494029304271108e+98
11
-2.5193242592864883e+168
-1.4178648401840193e+143
-1.35190676294417e+154

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
050151
161151
done61151

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.3s8769×body80valid
378.0ms2946×body80nan