Details

Time bar (total: 4.8s)

sample34.0ms

Algorithm
intervals
Results
14.0ms274×body80valid
3.0ms73×body80nan

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718
done17718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize87.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
7.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (111.0ms)

IterNodesCost
0227581
1878551
23814541
35002538
done5002538

prune278.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize91.0ms

Local error

Found 4 expressions with local error:

11.4b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
11.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (102.0ms)

IterNodesCost
0225725
1835631
23414609
35001589
done5001589

prune329.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize91.0ms

Local error

Found 4 expressions with local error:

8.0b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- flip3-+ neg-log flip-+
Counts
4 → 58
Calls
4 calls:
10.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Counts
70 → 70
Iterations

Useful iterations: 3 (103.0ms)

IterNodesCost
0232680
1883574
23567559
35001555
done5001555

prune320.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize95.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0129544
1469520
21914516
35002508
done5002508

prune381.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.6b

regimes225.0ms

Accuracy

93.6% (0.8b remaining)

Error of 8.5b against oracle of 7.7b and baseline of 19.8b

bsearch196.0ms

Steps
ItersRangePoint
9
1.4800420954007604e+99
2.6367850541344314e+108
5.663542808125347e+107
10
-6.90058054258779e+154
-1.4735496756669211e+144
-1.3326285121817453e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04960
14960
done4960

end0.0ms

sample920.0ms

Algorithm
intervals
Results
432.0ms8768×body80valid
143.0ms2904×body80nan