Details

Time bar (total: 5.2s)

sample34.0ms

Algorithm
intervals
Results
14.0ms274×body80valid
3.0ms73×body80nan

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318
done19318

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize85.0ms

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)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify59.0ms

Counts
152 → 152
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04062988
114311956
250021869
done50021869

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize87.0ms

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)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
13.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify182.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02831391
19981121
247231013
350011013
done50011013

prune434.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize86.0ms

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)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 76
Calls
4 calls:
12.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify114.0ms

Counts
88 → 88
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0249756
1969641
24038626
35001624
done5001624

prune426.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize92.0ms

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)))

rewrite49.0ms

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 expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Counts
80 → 80
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0139588
1510568
22129564
35001556
done5001556

prune422.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.6b

regimes228.0ms

Accuracy

93.6% (0.8b remaining)

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

bsearch188.0ms

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
05159
15159
done5159

end0.0ms

sample877.0ms

Algorithm
intervals
Results
419.0ms8768×body80valid
131.0ms2904×body80nan