Details

Time bar (total: 18.2s)

sample222.0ms

Algorithm
intervals
Results
55.0ms25×body1280valid
27.0ms43×body2560valid
24.0ms190×body80valid
9.0ms85×body80nan
7.0ms14×body640valid
4.0ms11×body320valid
2.0ms3×body5120valid
0.0ms2×body160valid

simplify36.0ms

Counts
1 → 1
Iterations
IterNodes
done34
534
432
330
223
115
010

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (* b_2 b_2) (* a c))
24.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
117.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
65.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
99.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
53.0ms
(- (* b_2 b_2) (* a c))
110.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
134 → 134
Iterations
IterNodes
done2000
32000
21291
1494
0199

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (* b_2 b_2) (* a c))
24.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 123
Calls
4 calls:
146.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
57.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
130.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms
(- (* b_2 b_2) (* a c))
94.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
135 → 135
Iterations
IterNodes
done2002
32002
21510
1560
0219

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (* b_2 b_2) (* a c))
24.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
85.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
120.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
49.0ms
(- (* b_2 b_2) (* a c))
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts
134 → 134
Iterations
IterNodes
done2000
32000
21291
1494
0199

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize64.0ms

Local error

Found 4 expressions with local error:

23.6b
(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))
25.3b
(cbrt (- (* b_2 b_2) (* a c)))
25.3b
(cbrt (- (* b_2 b_2) (* a c)))
25.3b
(cbrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))
9.0ms
(cbrt (- (* b_2 b_2) (* a c)))
10.0ms
(cbrt (- (* b_2 b_2) (* a c)))
9.0ms
(cbrt (- (* b_2 b_2) (* a c)))

series527.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))
117.0ms
(cbrt (- (* b_2 b_2) (* a c)))
112.0ms
(cbrt (- (* b_2 b_2) (* a c)))
132.0ms
(cbrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
71 → 71
Iterations
IterNodes
done2001
42001
31462
2502
1194
084

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

regimes256.0ms

Accuracy

82.2% (4.9b remaining)

Error of 10.3b against oracle of 5.3b and baseline of 32.9b

bsearch124.0ms

Steps
ItersRangePoint
10
1.3859530517218358e-142
9.527435083115218e-125
9.354082991670835e-125
8
-4.336983712965787e+155
-6.488343844980391e+152
-9.088000531423294e+152

simplify4.0ms

Iterations
IterNodes
done26
126
023

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.0s872×body1280valid
920.0ms1071×body2560valid
839.0ms5928×body80valid
302.0ms3004×body80nan
280.0ms471×body640valid
120.0ms109×body5120valid
66.0ms216×body320valid
23.0ms111×body160valid