Details

Time bar (total: 16.7s)

sample133.0ms

Algorithm
intervals
Results
40.0ms180×body80valid
24.0ms37×body1280valid
19.0ms24×body2560valid
12.0ms93×body80nan
11.0ms18×body640valid
4.0ms4×body5120valid
3.0ms6×body320valid
1.0ms4×body160valid

simplify133.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 3 a) c))
0.4b
(* (* 3 a) c)
1.7b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.3b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite91.0ms

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:
17.0ms
(- (* b b) (* (* 3 a) c))
29.0ms
(* (* 3 a) c)
31.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* b b) (* (* 3 a) c))
23.0ms
(* (* 3 a) c)
117.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
127.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.6s

Counts
96 → 96
Iterations
IterNodes
done2000
32000
21078
1353
0138

prune592.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.7b

localize66.0ms

Local error

Found 4 expressions with local error:

13.9b
(cbrt (* (* 3 a) c))
13.9b
(cbrt (* (* 3 a) c))
13.9b
(cbrt (* (* 3 a) c))
21.3b
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

rewrite85.0ms

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:
22.0ms
(cbrt (* (* 3 a) c))
21.0ms
(cbrt (* (* 3 a) c))
20.0ms
(cbrt (* (* 3 a) c))
20.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

series667.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (* (* 3 a) c))
174.0ms
(cbrt (* (* 3 a) c))
149.0ms
(cbrt (* (* 3 a) c))
202.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

simplify1.4s

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

prune528.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.7b

localize61.0ms

Local error

Found 4 expressions with local error:

13.9b
(cbrt (* (* 3 a) c))
13.9b
(cbrt (* (* 3 a) c))
13.9b
(cbrt (* (* 3 a) c))
21.3b
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))))

rewrite51.0ms

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:
10.0ms
(cbrt (* (* 3 a) c))
10.0ms
(cbrt (* (* 3 a) c))
13.0ms
(cbrt (* (* 3 a) c))
17.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))))

series635.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (* (* 3 a) c))
150.0ms
(cbrt (* (* 3 a) c))
154.0ms
(cbrt (* (* 3 a) c))
189.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))))

simplify1.3s

Counts
66 → 66
Iterations
IterNodes
done2003
42003
31515
2582
1223
095

prune570.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.6b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt b)
0.6b
(cbrt b)
21.3b
(sqrt (- (* b b) (* (* 3 a) c)))
22.1b
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (sqrt (- (* b b) (* (* 3 a) c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow1/3 sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 fma-udef flip--
Counts
4 → 57
Calls
4 calls:
1.0ms
(cbrt b)
1.0ms
(cbrt b)
27.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
1.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (sqrt (- (* b b) (* (* 3 a) c))))

series991.0ms

Counts
4 → 12
Calls
4 calls:
295.0ms
(cbrt b)
324.0ms
(cbrt b)
125.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
246.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (sqrt (- (* b b) (* (* 3 a) c))))

simplify1.2s

Counts
69 → 69
Iterations
IterNodes
done2001
32001
2641
1223
098

prune522.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 9.1b

regimes637.0ms

Accuracy

83.3% (4.1b remaining)

Error of 13.1b against oracle of 9.0b and baseline of 33.5b

bsearch252.0ms

Steps
ItersRangePoint
9
1.9857735944483347e-57
1.377205241174095e-49
4.989300060318096e-57
9
-6.068663549431906e+113
-2.857502301579116e+107
-2.6777729652842867e+110

simplify20.0ms

Iterations
IterNodes
done54
354
252
144
034

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.1s1061×body2560valid
939.0ms3001×body80nan
896.0ms5859×body80valid
818.0ms909×body1280valid
257.0ms471×body640valid
141.0ms108×body5120valid
91.0ms225×body320valid
29.0ms104×body160valid