Details

Time bar (total: 16.9s)

sample90.0ms

Algorithm
intervals
Results
36.0ms271×body80valid
14.0ms102×body80nan

simplify189.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02038
13638
26637
312237
416137
517437
617637
done17637

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize179.0ms

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)))

rewrite111.0ms

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×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log 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 → 151
Calls
4 calls:
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
108.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
163 → 163
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01796238
14404232
218333344
done50012696

prune959.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.8b

localize193.0ms

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)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×expm1-log1p-u cbrt-div flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×sqrt-prod
2×neg-mul-1 pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log
Counts
4 → 83
Calls
4 calls:
26.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms
(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)))

series564.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
163.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
148.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
95 → 95
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01782699
14462599
218692268
done50002232

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize202.0ms

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)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
172.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
141.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
147.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
74 → 74
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
0941258
12241190
27671076
342671058
done50001058

prune782.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.8b

localize152.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
12×add-cube-cbrt
10×fma-def
8×add-log-exp
6×associate-/r* times-frac
5×pow1
4×expm1-log1p-u cbrt-undiv distribute-rgt-neg-in div-exp log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×clear-num sum-log frac-2neg sqrt-div prod-exp cbrt-unprod div-inv distribute-lft-out associate-/l*
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sqrt-pow1 flip3-+ flip3-- pow1/2 neg-log associate-+l- flip-+ flip--
Counts
4 → 90
Calls
4 calls:
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* b -2)))
25.0ms
(/ (* a c) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
106.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* b -2)))
37.0ms
(/ (* a c) b)
131.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
102 → 102
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01761355
14651266
224811106
done50011101

prune742.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

regimes367.0ms

Accuracy

91.7% (1.1b remaining)

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

bsearch320.0ms

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
048149
157149
done57149

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.1s8769×body80valid
445.0ms2946×body80nan