Details

Time bar (total: 16.9s)

sample89.0ms

Algorithm
intervals
Results
32.0ms204×body80valid
12.0ms29×body2560valid
10.0ms31×body1280valid
8.0ms106×body80nan
3.0ms9×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify105.0ms

Counts
1 → 1
Iterations
IterNodes
done96
796
695
593
485
370
242
124
014

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- 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 → 84
Calls
4 calls:
105.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
6.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
86.0ms
(- (* b b) (* (* 4.0 a) c))
123.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
96 → 96
Iterations
IterNodes
done5001
21142
1388
0158

prune698.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1 distribute-lft-out--
4×flip3-- 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 → 83
Calls
4 calls:
50.0ms
(/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
13.0ms
(- (* b b) (* (* 4.0 a) c))
53.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
54.0ms
(- (* b b) (* (* 4.0 a) c))
122.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
95 → 95
Iterations
IterNodes
done5007
34048
21047
1347
0153

prune708.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
18×*-un-lft-identity
13×associate-*r* add-exp-log add-cube-cbrt
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1
6×associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp 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 → 85
Calls
4 calls:
141.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
13.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
81.0ms
(- (* b b) (* (* 4.0 a) c))
114.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
97 → 97
Iterations
IterNodes
done5002
21413
1453
0178

prune615.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- 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 → 84
Calls
4 calls:
114.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
12.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
69.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
96 → 96
Iterations
IterNodes
done5001
21142
1388
0158

prune500.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

regimes513.0ms

Accuracy

84.3% (4.5b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 34.4b

bsearch179.0ms

Steps
ItersRangePoint
8
1.5119020269574885e-23
1.8921341643334238e-20
9.136492990928292e-23
6
-1.7989235910837076e+89
-1.4585470499056154e+88
-1.7633154797394035e+89

simplify10.0ms

Iterations
IterNodes
done34
134
029

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s5865×body80valid
756.0ms2875×body80nan
573.0ms1057×body2560valid
385.0ms902×body1280valid
171.0ms434×body640valid
69.0ms124×body5120valid
51.0ms224×body320valid
16.0ms112×body160valid