Details

Time bar (total: 20.4s)

sample68.0ms

Algorithm
intervals
Results
37.0ms283×body80valid
8.0ms69×body80nan

simplify247.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
02038
13638
26637
312237
415437
516637
616837
done16837

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize112.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
18.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
38.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(- (* b b) (* (* 4.0 a) c))
133.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.4s

Counts
78 → 78
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0711146
11681050
2574952
32407952
done5000936

prune555.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize164.0ms

Local error

Found 4 expressions with local error:

9.7b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div add-log-exp
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2 prod-diff
1×sub-neg fma-neg diff-log difference-of-squares
Counts
4 → 70
Calls
4 calls:
68.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
82 → 82
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01041631
12541137
27301072
326911064
done50011053

prune543.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize157.0ms

Local error

Found 4 expressions with local error:

9.4b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

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:
16.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
34.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
100 → 100
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01152639
12821649
28591574
333301538
done50001535

prune574.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize160.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 97
Calls
4 calls:
110.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
168.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
156.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
193.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
109 → 109
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01933874
13603353
27612692
322752632
done50002554

prune676.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

regimes230.0ms

Accuracy

89.9% (1.2b remaining)

Error of 8.8b against oracle of 7.5b and baseline of 19.9b

bsearch296.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
10
-2.386196042261592e+160
-1.0923850232644114e+143
-1.3255191511081353e+154

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
044137
149137
done49137

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.7s8735×body80valid
315.0ms2941×body80nan