Details

Time bar (total: 20.3s)

sample57.0ms

Algorithm
intervals
Results
25.0ms282×body80valid
6.0ms80×body80nan

simplify242.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize125.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.6b
(- (* b b) (* (* 4.0 a) c))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

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:
20.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (* b b) (* (* 4.0 a) c))
52.0ms
(- (* b b) (* (* 4.0 a) c))
130.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
78 → 78
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0711146
11681050
2574952
32407952
done5000936

prune537.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize143.0ms

Local error

Found 4 expressions with local error:

8.4b
(+ (- 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)))

rewrite68.0ms

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))))))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
122.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts
88 → 88
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0901548
12471095
28411019
330481007
done50001005

prune711.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize165.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite139.0ms

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:
95.0ms
(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)))
20.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
136.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
178.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
155.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
109 → 109
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01933874
13603353
27612692
322752632
done50002554

prune753.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

localize180.0ms

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)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

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:
22.0ms
(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)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series967.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
156.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
587.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
76 → 76
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0941248
12161148
26171052
321591040
done50011016

prune563.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.9b

regimes239.0ms

Accuracy

92.8% (0.9b remaining)

Error of 8.6b against oracle of 7.7b and baseline of 20.3b

bsearch109.0ms

Steps
ItersRangePoint
0
2.0836136179885362e+135
2.1675125417143413e+135
2.1255630798514387e+135
9
-1.489991982892314e+158
-2.0545059602165346e+153
-1.3596485852230119e+154

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
043143
152143
done52143

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s8687×body80valid
320.0ms2888×body80nan