Details

Time bar (total: 14.7s)

sample55.0ms

Algorithm
intervals
Results
16.0ms41×body2560valid
8.0ms178×body80valid
7.0ms29×body1280valid
4.0ms93×body80nan
3.0ms17×body640valid
0.0ms5×body160valid
0.0ms1×body5120valid
0.0ms2×body320valid

simplify98.0ms

Counts
1 → 1
Iterations
IterNodes
done102
7102
6101
599
491
375
240
122
012

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.7b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(- (* b b) (* (* 3.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
81.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms
(- (* b b) (* (* 3.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
105.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
60.0ms
(- (* b b) (* (* 3.0 a) c))
117.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
102 → 102
Iterations
IterNodes
done5000
21406
1437
0167

prune808.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 3.0 a) (- (sqrt (- (* b b) (* c (* 3.0 a)))) b))
1.7b
(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
2.0b
(- (* b b) (* c (* 3.0 a)))
23.9b
(sqrt (- (* b b) (* c (* 3.0 a))))

rewrite131.0ms

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-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
6×associate-/r* times-frac difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 105
Calls
4 calls:
58.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* c (* 3.0 a)))) b))
48.0ms
(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
7.0ms
(- (* b b) (* c (* 3.0 a)))
14.0ms
(sqrt (- (* b b) (* c (* 3.0 a))))

series595.0ms

Counts
4 → 12
Calls
4 calls:
308.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* c (* 3.0 a)))) b))
98.0ms
(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
63.0ms
(- (* b b) (* c (* 3.0 a)))
127.0ms
(sqrt (- (* b b) (* c (* 3.0 a))))

simplify1.9s

Counts
117 → 117
Iterations
IterNodes
done5001
21522
1497
0187

prune615.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* c (* 3.0 a))
1.7b
(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
2.0b
(- (* b b) (* c (* 3.0 a)))
23.9b
(sqrt (- (* b b) (* c (* 3.0 a))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff
16×sqrt-prod
10×pow1
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*l* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
17.0ms
(* c (* 3.0 a))
55.0ms
(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
14.0ms
(- (* b b) (* c (* 3.0 a)))
16.0ms
(sqrt (- (* b b) (* c (* 3.0 a))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* c (* 3.0 a))
110.0ms
(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
56.0ms
(- (* b b) (* c (* 3.0 a)))
88.0ms
(sqrt (- (* b b) (* c (* 3.0 a))))

simplify2.5s

Counts
106 → 106
Iterations
IterNodes
done5000
33888
21068
1399
0160

prune431.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* 3.0 a))
1.7b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(- (* b b) (* (* 3.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
14×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube
8×pow1
4×expm1-log1p-u distribute-rgt-neg-in div-exp log1p-expm1-u
3×distribute-lft-neg-in times-frac prod-exp sqrt-prod associate-/l*
2×cbrt-undiv rec-exp sum-log flip3-- sqrt-div 1-exp pow-flip flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff pow-prod-down neg-log associate-+l- cbrt-unprod flip-+ div-inv inv-pow
Counts
4 → 90
Calls
4 calls:
9.0ms
(/ 1 (* 3.0 a))
20.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ 1 (* 3.0 a))
105.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
58.0ms
(- (* b b) (* (* 3.0 a) c))
98.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.0s

Counts
102 → 102
Iterations
IterNodes
done5000
21241
1375
0152

prune483.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.0b

regimes565.0ms

Accuracy

85.2% (4.3b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 34.9b

bsearch168.0ms

Steps
ItersRangePoint
10
8.767897341253802e-114
4.657027509742155e-104
4.6129908231112306e-104
9
-6.117539429929052e+154
-3.6285784997486435e+148
-6.386028720359615e+148

simplify7.0ms

Iterations
IterNodes
done36
136
030

end0.0ms

sample2.6s

Algorithm
intervals
Results
888.0ms1115×body2560valid
500.0ms5808×body80valid
332.0ms901×body1280valid
203.0ms2954×body80nan
189.0ms455×body640valid
46.0ms105×body5120valid
38.0ms213×body320valid
14.0ms124×body160valid