Details

Time bar (total: 15.0s)

sample68.0ms

Algorithm
intervals
Results
27.0ms278×body80valid
9.0ms108×body80nan

simplify246.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
02038
13938
27937
314337
417937
518937
619337
done19337

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize127.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
55.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
29.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series514.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
143.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
163 → 163
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01796238
14414232
218153344
done50012696

prune705.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize198.0ms

Local error

Found 4 expressions with local error:

10.5b
(- (- b) (* (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
23.3b
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

rewrite71.0ms

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
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 flip3-- sqrt-div diff-log flip--
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 84
Calls
4 calls:
30.0ms
(- (- b) (* (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
30.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
3.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(- (- b) (* (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
123.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
156.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

simplify1.3s

Counts
96 → 96
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01322443
13161485
212491422
done50001407

prune802.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize163.0ms

Local error

Found 4 expressions with local error:

9.0b
(+ (- b) (* (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
23.3b
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
23.3b
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

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
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2
2×sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-- flip3-+ neg-log flip-- flip-+
Counts
4 → 72
Calls
4 calls:
33.0ms
(+ (- b) (* (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
3.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
3.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(+ (- b) (* (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
126.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
121.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
126.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify994.0ms

Counts
84 → 84
Iterations

Useful iterations: done (991.0ms)

IterNodesCost
01071352
1282931
21182867
done5001864

prune733.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize164.0ms

Local error

Found 4 expressions with local error:

23.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
24.1b
(cbrt (fma (* 4.0 a) (- c) (pow b 2)))
24.1b
(cbrt (fma (* 4.0 a) (- c) (pow b 2)))

rewrite22.0ms

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 add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 sqrt-div
1×flip3-- flip--
Counts
4 → 58
Calls
4 calls:
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
1.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
1.0ms
(cbrt (fma (* 4.0 a) (- c) (pow b 2)))
1.0ms
(cbrt (fma (* 4.0 a) (- c) (pow b 2)))

series864.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
124.0ms
(sqrt (fma (* 4.0 a) (- c) (pow b 2)))
321.0ms
(cbrt (fma (* 4.0 a) (- c) (pow b 2)))
292.0ms
(cbrt (fma (* 4.0 a) (- c) (pow b 2)))

simplify805.0ms

Counts
70 → 70
Iterations

Useful iterations: done (801.0ms)

IterNodesCost
01101012
1254936
2896872
done5001860

prune795.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

regimes325.0ms

Accuracy

93% (0.9b remaining)

Error of 8.1b against oracle of 7.3b and baseline of 19.6b

bsearch287.0ms

Steps
ItersRangePoint
6
1.9101351599902807e+102
2.525038855038462e+103
1.2511509099731475e+103
9
-2.501158360438979e+160
-5.198860796817705e+153
-1.347978711569674e+154

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
046133
154133
done54133

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.7s8709×body80valid
363.0ms2896×body80nan