Details

Time bar (total: 5.5s)

sample34.0ms

Algorithm
intervals
Results
14.0ms276×body80valid
3.0ms73×body80nan

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718
done17718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize84.0ms

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))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

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))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (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)))

simplify60.0ms

Counts
152 → 152
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04062988
114311956
250021869
done50021869

prune406.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize88.0ms

Local error

Found 4 expressions with local error:

10.2b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

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:
13.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
77.0ms
(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)))

simplify116.0ms

Counts
88 → 88
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0249756
1969641
24038626
35001624
done5001624

prune440.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize97.0ms

Local error

Found 4 expressions with local error:

21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u cbrt-div flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 64
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Counts
76 → 76
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0215634
1688602
22689596
35001594
done5001594

prune500.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

localize94.0ms

Local error

Found 4 expressions with local error:

7.5b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×sqrt-prod
2×neg-mul-1 pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 83
Calls
4 calls:
15.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
121.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Counts
95 → 95
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04281492
116671341
250021297
done50021297

prune503.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.6b

regimes255.0ms

Accuracy

92.2% (0.9b remaining)

Error of 8.5b against oracle of 7.6b and baseline of 19.5b

bsearch184.0ms

Steps
ItersRangePoint
6
1.4800420954007604e+99
6.083502279918113e+99
4.0105183182160945e+99
10
-4.9909276054097234e+78
-4.785667473127655e+65
-4.287313385232319e+78

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05159
15159
done5159

end0.0ms

sample966.0ms

Algorithm
intervals
Results
466.0ms8703×body80valid
143.0ms2871×body80nan