Details

Time bar (total: 17.5s)

sample109.0ms

Algorithm
intervals
Results
40.0ms190×body80valid
22.0ms43×body2560valid
11.0ms25×body1280valid
8.0ms85×body80nan
5.0ms11×body320valid
5.0ms13×body640valid
2.0ms3×body5120valid
0.0ms2×body160valid

simplify128.0ms

Counts
1 → 1
Iterations
IterNodes
done102
7102
6101
599
491
373
241
122
012

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3 a) c)
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.0b
(- (* b b) (* (* 3 a) c))
24.5b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative associate-+l- flip-+
Counts
4 → 84
Calls
4 calls:
14.0ms
(* (* 3 a) c)
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
17.0ms
(- (* b b) (* (* 3 a) c))
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (* 3 a) c)
94.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
53.0ms
(- (* b b) (* (* 3 a) c))
102.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts
96 → 96
Iterations
IterNodes
done2000
32000
21077
1353
0138

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.4b

localize52.0ms

Local error

Found 4 expressions with local error:

16.7b
(cbrt (* (* 3 a) c))
16.7b
(cbrt (* (* 3 a) c))
16.7b
(cbrt (* (* 3 a) c))
24.5b
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 54
Calls
4 calls:
20.0ms
(cbrt (* (* 3 a) c))
20.0ms
(cbrt (* (* 3 a) c))
19.0ms
(cbrt (* (* 3 a) c))
19.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

series574.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(cbrt (* (* 3 a) c))
131.0ms
(cbrt (* (* 3 a) c))
143.0ms
(cbrt (* (* 3 a) c))
192.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

simplify1.3s

Counts
66 → 66
Iterations
IterNodes
done2060
42060
31778
2527
1217
093

prune963.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.4b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c))))
16.7b
(cbrt (* (* 3 a) c))
16.7b
(cbrt (* (* 3 a) c))
24.5b
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-log-exp
5×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×sqrt-prod
2×cbrt-prod flip3-- pow1/3 sqrt-div flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 59
Calls
4 calls:
9.0ms
(- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c))))
17.0ms
(cbrt (* (* 3 a) c))
19.0ms
(cbrt (* (* 3 a) c))
21.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c)))))

series915.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c))))
121.0ms
(cbrt (* (* 3 a) c))
142.0ms
(cbrt (* (* 3 a) c))
443.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt (* 3 a)) (cbrt c)))))

simplify1.3s

Counts
71 → 71
Iterations
IterNodes
done2001
32001
2936
1302
0125

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.9b

localize39.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 3 a) c))
24.5b
(sqrt (- (* b b) (* (* 3 a) c)))
24.5b
(sqrt (- (* b b) (* (* 3 a) c)))
24.5b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 71
Calls
4 calls:
8.0ms
(- (* b b) (* (* 3 a) c))
13.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (* b b) (* (* 3 a) c))
107.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
124.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify915.0ms

Counts
83 → 83
Iterations
IterNodes
done2001
32001
2563
1177
072

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.8b

regimes611.0ms

Accuracy

85.4% (3.2b remaining)

Error of 14.2b against oracle of 11.0b and baseline of 33.1b

bsearch282.0ms

Steps
ItersRangePoint
8
2.667754917997735e-29
4.030937871461662e-25
6.134174794339903e-27
9
-4.758281296322139e+130
-8.621942972151158e+124
-3.539544285799822e+127

simplify12.0ms

Iterations
IterNodes
done55
155
042

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.2s5928×body80valid
1.0s1069×body2560valid
648.0ms874×body1280valid
498.0ms108×body5120valid
359.0ms3004×body80nan
329.0ms467×body640valid
148.0ms219×body320valid
31.0ms109×body160valid