Details

Time bar (total: 15.8s)

sample77.0ms

Algorithm
intervals
Results
36.0ms285×body80valid
10.0ms89×body80nan

simplify216.0ms

Counts
1 → 1
Iterations
IterNodes
done193
6193
5189
4179
3143
279
139
020

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize154.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
12.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (* b b) (* (* 4.0 a) c))
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
78 → 78
Iterations
IterNodes
done5001
2858
1185
071

prune647.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.4b

localize166.0ms

Local error

Found 4 expressions with local error:

9.5b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×fma-def *-un-lft-identity add-cube-cbrt
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative neg-mul-1 flip3-+ neg-log associate-+l- flip-+
Counts
4 → 76
Calls
4 calls:
19.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
134.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
88 → 88
Iterations
IterNodes
done5000
21106
1260
090

prune927.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.4b

localize246.0ms

Local error

Found 4 expressions with local error:

10.9b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
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×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
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:
27.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done5001
21219
1293
0115

prune971.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize165.0ms

Local error

Found 4 expressions with local error:

22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
165.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
111.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
147.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
74 → 74
Iterations
IterNodes
done5000
34267
2767
1224
094

prune745.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.8b

regimes505.0ms

Accuracy

92.8% (0.9b remaining)

Error of 8.1b against oracle of 7.1b and baseline of 20.3b

bsearch163.0ms

Steps
ItersRangePoint
5
2.6243927093659187e+107
5.901159163981397e+107
3.9321910650396994e+107
4
-2.6709732094199134e+112
-1.6569790030408257e+112
-2.630943794196583e+112

simplify11.0ms

Iterations
IterNodes
done49
149
043

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.4s8696×body80valid
295.0ms2883×body80nan