Details

Time bar (total: 13.6s)

sample152.0ms

Algorithm
intervals
Results
36.0ms36×body2560valid
32.0ms187×body80valid
31.0ms26×body1280valid
13.0ms84×body80nan
8.0ms12×body640valid
4.0ms8×body320valid
4.0ms3×body5120valid
2.0ms5×body160valid

simplify104.0ms

Counts
1 → 1
Iterations
IterNodes
done95
795
694
592
484
367
243
124
014

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
1.0b
(- (* b b) (* (* 4 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite133.0ms

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-- insert-posit16 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 → 88
Calls
4 calls:
74.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
11.0ms
(- (* b b) (* (* 4 a) c))
31.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
71.0ms
(- (* b b) (* (* 4 a) c))
124.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
94.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify856.0ms

Counts
100 → 100
Iterations
IterNodes
done2000
21158
1394
0161

prune497.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
1.0b
(- (* b b) (* (* 4 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
24×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×insert-posit16
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 166
Calls
4 calls:
55.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
14.0ms
(- (* b b) (* (* 4 a) c))
34.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
60.0ms
(- (* b b) (* (* 4 a) c))
101.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
106.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.0s

Counts
178 → 178
Iterations
IterNodes
done2001
21712
1648
0265

prune737.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
33.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
42.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
147.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
100.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
128.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify504.0ms

Counts
76 → 76
Iterations
IterNodes
done2002
2595
1194
082

prune604.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.1b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
48.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
35.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
94.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
85.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify564.0ms

Counts
76 → 76
Iterations
IterNodes
done2002
2595
1194
082

prune544.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.1b

regimes312.0ms

Accuracy

84.8% (4.4b remaining)

Error of 9.6b against oracle of 5.2b and baseline of 33.9b

bsearch561.0ms

Steps
ItersRangePoint
8
2.469533614662255e-16
6.384179586440732e-13
5.297236684235463e-16
9
2.201345904528094e-30
9.673336284784144e-25
1.8656332031849816e-25
10
5.0092461758030895e-88
5.0325836698121444e-76
1.739098950628615e-79
9
-7.806260788625035e+148
-1.2289413495061505e+143
-1.6844644503075447e+144

simplify18.0ms

Iterations
IterNodes
done46
346
243
140
033

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.7s5761×body80valid
995.0ms1103×body2560valid
734.0ms957×body1280valid
476.0ms2981×body80nan
237.0ms480×body640valid
115.0ms115×body5120valid
104.0ms223×body320valid
32.0ms128×body160valid