Details

Time bar (total: 16.1s)

sample97.0ms

Algorithm
intervals
Results
22.0ms204×body80valid
14.0ms29×body2560valid
13.0ms31×body1280valid
9.0ms106×body80nan
3.0ms9×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify136.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
379
243
125
014

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0)
0.8b
(- (* b b) (* 4.0 (* c a)))
0.8b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
24.3b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite247.0ms

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-- 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 → 118
Calls
4 calls:
128.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0)
14.0ms
(- (* b b) (* 4.0 (* c a)))
85.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
17.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0)
88.0ms
(- (* b b) (* 4.0 (* c a)))
117.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
124.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify1.5s

Counts
130 → 130
Iterations
IterNodes
done5001
21466
1493
0194

prune647.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* c a)))) b))
0.8b
(- (* b b) (* 4.0 (* c a)))
0.8b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
24.3b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite109.0ms

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×associate-/r* add-cbrt-cube add-exp-log
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 117
Calls
4 calls:
42.0ms
(/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* c a)))) b))
8.0ms
(- (* b b) (* 4.0 (* c a)))
47.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
10.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* c a)))) b))
56.0ms
(- (* b b) (* 4.0 (* c a)))
150.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
125.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify1.5s

Counts
129 → 129
Iterations
IterNodes
done5001
21631
1487
0199

prune536.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
0.8b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
24.3b
(sqrt (- (* b b) (* 4.0 (* c a))))
24.3b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite407.0ms

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 flip3-- add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
39.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
347.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
9.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series365.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
96.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
86.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
86.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify2.5s

Counts
128 → 128
Iterations
IterNodes
done5001
33517
2901
1292
0113

prune566.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

localize68.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
24.3b
(sqrt (- (* b b) (* 4.0 (* c a))))
24.3b
(sqrt (- (* b b) (* 4.0 (* c a))))
24.3b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite70.0ms

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 sqrt-div add-log-exp
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg diff-log distribute-lft-out--
Counts
4 → 92
Calls
4 calls:
40.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
9.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
83.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
84.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify2.5s

Counts
104 → 104
Iterations
IterNodes
done5001
33517
2901
1292
0113

prune541.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.7b

regimes283.0ms

Accuracy

85.4% (3.5b remaining)

Error of 14.2b against oracle of 10.7b and baseline of 34.5b

bsearch106.0ms

Steps
ItersRangePoint
5
4.244596206919672e-17
1.6775967427727985e-16
5.86022363894318e-17
6
-1.7989235910837076e+89
-1.4585470499056154e+88
-1.7633154797394035e+89

simplify7.0ms

Iterations
IterNodes
done37
137
032

end0.0ms

sample2.5s

Algorithm
intervals
Results
565.0ms2875×body80nan
557.0ms5865×body80valid
361.0ms1057×body2560valid
335.0ms902×body1280valid
93.0ms434×body640valid
52.0ms112×body160valid
47.0ms124×body5120valid
35.0ms224×body320valid