Details

Time bar (total: 15.3s)

sample112.0ms

Algorithm
intervals
Results
27.0ms80×body80nan
19.0ms43×body2560valid
13.0ms165×body80valid
13.0ms32×body1280valid
5.0ms16×body640valid
5.0ms8×body5120valid
2.0ms7×body320valid
1.0ms5×body160valid

simplify74.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* 3.0 a) c)
0.7b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite174.0ms

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:
18.0ms
(* (* 3.0 a) c)
115.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
28.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series410.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (* 3.0 a) c)
137.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
128.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
104.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.3s

Counts
106 → 106
Iterations
IterNodes
done5001
22631
1472
0172

prune726.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune54.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
0.5b
(* (* 3.0 a) c)
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×*-un-lft-identity
18×add-cbrt-cube
15×add-sqr-sqrt
13×prod-exp
12×pow1 add-cube-cbrt
10×fma-def associate-*r*
8×add-log-exp
7×cbrt-unprod
6×associate-*l*
5×distribute-rgt-neg-in
4×expm1-log1p-u div-exp pow-prod-down log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in flip3-+ times-frac sqrt-prod flip-+
2×frac-times cbrt-undiv rec-exp sum-log sqrt-div 1-exp associate-*l/ *-commutative
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sqrt-pow1 flip3-- pow1/2 neg-log associate-*r/ un-div-inv associate-+l- div-inv flip-- unswap-sqr
Counts
4 → 104
Calls
4 calls:
99.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
22.0ms
(* (* 3.0 a) c)
30.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
36.0ms
(* (* 3.0 a) c)
108.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
109.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.5s

Counts
116 → 116
Iterations
IterNodes
done5001
23500
1558
0199

prune690.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (- (sqrt (- (* b b) (* a (* 3.0 c)))) b) 3.0) (/ 1 a))
0.3b
(/ (- (sqrt (- (* b b) (* a (* 3.0 c)))) b) 3.0)
1.5b
(- (sqrt (- (* b b) (* a (* 3.0 c)))) b)
21.2b
(sqrt (- (* b b) (* a (* 3.0 c))))

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
65×*-un-lft-identity
52×times-frac
47×add-cube-cbrt
28×add-exp-log
23×sqrt-prod
22×associate-*l*
18×add-cbrt-cube prod-diff
16×difference-of-squares
13×associate-*r*
9×div-exp
8×prod-exp distribute-lft-out--
7×pow1
6×fma-neg associate-/l* add-log-exp unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×associate-/r* flip3-- div-inv flip--
2×rec-exp sqrt-div 1-exp associate-/l/
1×frac-times rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative
Counts
4 → 170
Calls
4 calls:
133.0ms
(* (/ (- (sqrt (- (* b b) (* a (* 3.0 c)))) b) 3.0) (/ 1 a))
129.0ms
(/ (- (sqrt (- (* b b) (* a (* 3.0 c)))) b) 3.0)
46.0ms
(- (sqrt (- (* b b) (* a (* 3.0 c)))) b)
9.0ms
(sqrt (- (* b b) (* a (* 3.0 c))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (/ (- (sqrt (- (* b b) (* a (* 3.0 c)))) b) 3.0) (/ 1 a))
141.0ms
(/ (- (sqrt (- (* b b) (* a (* 3.0 c)))) b) 3.0)
106.0ms
(- (sqrt (- (* b b) (* a (* 3.0 c)))) b)
106.0ms
(sqrt (- (* b b) (* a (* 3.0 c))))

simplify2.1s

Counts
182 → 182
Iterations
IterNodes
done5000
23712
1817
0283

prune877.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.6b

regimes674.0ms

Accuracy

87.6% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 39.5b

bsearch71.0ms

Steps
ItersRangePoint
2
3.964947473899983e-62
4.720485511979589e-62
4.626043257219638e-62
7
-5.856362438573669e+138
-1.280729871585891e+137
-2.3037792410978802e+138

simplify7.0ms

Iterations
IterNodes
done38
138
029

end0.0ms

sample3.0s

Algorithm
intervals
Results
835.0ms5793×body80valid
609.0ms1095×body2560valid
385.0ms887×body1280valid
308.0ms2874×body80nan
148.0ms468×body640valid
51.0ms107×body5120valid
46.0ms243×body320valid
15.0ms115×body160valid