Details

Time bar (total: 15.9s)

sample93.0ms

Algorithm
intervals
Results
47.0ms283×body80valid
10.0ms96×body80nan

simplify243.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize137.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff sqrt-prod
8×add-log-exp
7×fma-neg
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log difference-of-squares
1×distribute-lft-out--
Counts
4 → 91
Calls
4 calls:
10.0ms
(- (* b b) (* (* 4.0 a) c))
64.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.4s

Counts
103 → 103
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01302001
12961668
28451450
333891362
done50001305

prune634.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.4b

localize160.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
5.2b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.6b
(/ (* a c) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
32×add-sqr-sqrt
23×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-exp-log add-cbrt-cube
9×times-frac
7×associate-/l*
6×fma-neg add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 113
Calls
4 calls:
81.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
94.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
21.0ms
(/ (* a c) b)
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
89.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
34.0ms
(/ (* a c) b)
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
125 → 125
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02172386
15442081
219591775
done50011679

prune587.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize146.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/r* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 105
Calls
4 calls:
50.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
15.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
274.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
69.0ms
(- (* b b) (* (* 4.0 a) c))
98.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
117 → 117
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01862435
14392125
213421819
done50001750

prune482.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

localize110.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/r*
19×prod-diff
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- div-exp flip-- associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r/
Counts
4 → 182
Calls
4 calls:
45.0ms
(/ 2.0 (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) c))
9.0ms
(- (* b b) (* (* 4.0 a) c))
66.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ 2.0 (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) c))
64.0ms
(- (* b b) (* (* 4.0 a) c))
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
194 → 194
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03154975
17244566
221464241
done50004168

prune845.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.7b

regimes324.0ms

Accuracy

91.9% (1.3b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 21.3b

bsearch268.0ms

Steps
ItersRangePoint
9
1.2073698495971617e+61
8.75865749938149e+67
2.46028134553803e+67
10
-3.742210988141449e+103
-1.0235731023437291e+92
-3.359953003549157e+103

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
042142
149142
done49142

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.2s8706×body80valid
351.0ms2844×body80nan