Details

Time bar (total: 15.5s)

sample85.0ms

Algorithm
intervals
Results
18.0ms40×body2560valid
14.0ms183×body80valid
13.0ms35×body1280valid
6.0ms79×body80nan
5.0ms16×body640valid
1.0ms2×body5120valid
1.0ms5×body160valid
1.0ms2×body320valid

simplify74.0ms

Counts
1 → 1
Iterations
IterNodes
done120
5120
4112
383
242
122
012

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b
(* (* 3.0 a) c)
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
11×add-cube-cbrt
10×pow1 fma-def
8×add-log-exp
6×distribute-rgt-neg-in distribute-lft-out
5×times-frac associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ sqrt-div div-exp associate-+l- flip-+ associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 frac-2neg sqrt-pow1 flip3-- pow1/2 div-sub associate-*l* neg-log *-commutative div-inv flip--
Counts
4 → 94
Calls
4 calls:
89.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
28.0ms
(* (* 3.0 a) c)
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
28.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
37.0ms
(* (* 3.0 a) c)
133.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
86.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts
106 → 106
Iterations
IterNodes
done5002
22638
1473
0172

prune801.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.3b
(fma b b (- (* (* 3.0 a) c)))
1.3b
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
24.2b
(sqrt (fma b b (- (* (* 3.0 a) c))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
10×pow1
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*l* *-commutative fma-udef flip-- distribute-lft-out--
Counts
4 → 86
Calls
4 calls:
13.0ms
(* (* 3.0 a) c)
0.0ms
(fma b b (- (* (* 3.0 a) c)))
9.0ms
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
2.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))

series371.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (* 3.0 a) c)
73.0ms
(fma b b (- (* (* 3.0 a) c)))
138.0ms
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
125.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))

simplify926.0ms

Counts
98 → 98
Iterations
IterNodes
done5001
21387
1329
0141

prune676.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize62.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
1.3b
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
24.2b
(sqrt (fma b b (- (* (* 3.0 a) c))))
24.2b
(sqrt (fma b b (- (* (* 3.0 a) c))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 112
Calls
4 calls:
17.0ms
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
21.0ms
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
2.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))
3.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
131.0ms
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
120.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))
151.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))

simplify1.5s

Counts
124 → 124
Iterations
IterNodes
done5000
32648
2655
1228
0100

prune873.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.7b

localize41.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
24.2b
(sqrt (fma b b (- (* (* 3.0 a) c))))
24.2b
(sqrt (fma b b (- (* (* 3.0 a) c))))
24.2b
(sqrt (fma b b (- (* (* 3.0 a) c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×*-un-lft-identity
22×sqrt-prod
21×add-cube-cbrt
18×prod-diff
7×pow1
6×fma-neg add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 86
Calls
4 calls:
18.0ms
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
2.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))
2.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))
3.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))

series496.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (sqrt (fma b b (- (* (* 3.0 a) c)))) b)
132.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))
126.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))
118.0ms
(sqrt (fma b b (- (* (* 3.0 a) c))))

simplify1.3s

Counts
98 → 98
Iterations
IterNodes
done5000
32648
2655
1228
0100

prune696.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.7b

regimes710.0ms

Accuracy

84.6% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 34.6b

bsearch202.0ms

Steps
ItersRangePoint
7
1.726360512453143e-63
2.3465896586148578e-61
8.08526583505735e-63
9
-3.845605078781637e+76
-1.2146338677939432e+68
-7.943482039519134e+75

simplify8.0ms

Iterations
IterNodes
done45
245
137
029

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.0s1095×body2560valid
769.0ms2884×body80nan
665.0ms5775×body80valid
371.0ms933×body1280valid
137.0ms446×body640valid
136.0ms228×body320valid
51.0ms92×body5120valid
17.0ms127×body160valid