Details

Time bar (total: 8.2s)

sample38.0ms

Algorithm
intervals
Results
8.0ms39×body2560valid
6.0ms36×body1280valid
6.0ms165×body80valid
3.0ms86×body80nan
2.0ms13×body640valid
1.0msbody320valid
1.0msbody5120valid
0.0msbody160valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12217
24216
38316
410216
511016
done11016

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.0b
(- (* b b) (* (* 3.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×pow1 add-sqr-sqrt fma-def add-log-exp
add-exp-log add-cube-cbrt add-cbrt-cube
expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
flip3-- sqrt-div sum-log flip-- distribute-lft-out
+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative flip-+
Counts
4 → 80
Calls
4 calls:
6.0ms
(* (* 3.0 a) c)
3.0ms
(- (* b b) (* (* 3.0 a) c))
15.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
45.0ms
(- (* b b) (* (* 3.0 a) c))
74.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify496.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
01351109
13511006
21323900
done5001900

prune257.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* c (* 3.0 a))
1.3b
(fma b b (- (* c (* 3.0 a))))
1.4b
(+ (- b) (sqrt (fma b b (- (* c (* 3.0 a))))))
22.6b
(sqrt (fma b b (- (* c (* 3.0 a)))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×pow1 add-sqr-sqrt fma-def
add-exp-log add-cube-cbrt add-cbrt-cube
add-log-exp
expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
distribute-lft-neg-in associate-*l* pow-prod-down prod-exp sqrt-prod cbrt-unprod
sum-log distribute-lft-out
+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* neg-log *-commutative flip-+ fma-udef
Counts
4 → 72
Calls
4 calls:
6.0ms
(* c (* 3.0 a))
0.0ms
(fma b b (- (* c (* 3.0 a))))
8.0ms
(+ (- b) (sqrt (fma b b (- (* c (* 3.0 a))))))
1.0ms
(sqrt (fma b b (- (* c (* 3.0 a)))))

series233.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* c (* 3.0 a))
53.0ms
(fma b b (- (* c (* 3.0 a))))
86.0ms
(+ (- b) (sqrt (fma b b (- (* c (* 3.0 a))))))
77.0ms
(sqrt (fma b b (- (* c (* 3.0 a)))))

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: 3 (274.0ms)

IterNodesCost
0114916
1272846
2837751
32873741
done5000741

prune233.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.3b

localize15.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (* c (* 3.0 a)))
15.3b
(cbrt (* c (* 3.0 a)))
15.3b
(cbrt (* c (* 3.0 a)))
22.6b
(sqrt (fma b b (- (* (* (cbrt (* c (* 3.0 a))) (cbrt (* c (* 3.0 a)))) (cbrt (* c (* 3.0 a)))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity
add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
cbrt-prod pow1/3 sqrt-prod
rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 48
Calls
4 calls:
4.0ms
(cbrt (* c (* 3.0 a)))
4.0ms
(cbrt (* c (* 3.0 a)))
4.0ms
(cbrt (* c (* 3.0 a)))
1.0ms
(sqrt (fma b b (- (* (* (cbrt (* c (* 3.0 a))) (cbrt (* c (* 3.0 a)))) (cbrt (* c (* 3.0 a)))))))

series594.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(cbrt (* c (* 3.0 a)))
265.0ms
(cbrt (* c (* 3.0 a)))
94.0ms
(cbrt (* c (* 3.0 a)))
141.0ms
(sqrt (fma b b (- (* (* (cbrt (* c (* 3.0 a))) (cbrt (* c (* 3.0 a)))) (cbrt (* c (* 3.0 a)))))))

simplify1.2s

Counts
60 → 60
Iterations

Useful iterations: 4 (344.0ms)

IterNodesCost
077896
1161833
2341589
3884529
42973498
done5001498

prune221.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.3b

localize21.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (* c (* 3.0 a)))
15.3b
(cbrt (* c (* 3.0 a)))
15.3b
(cbrt (* a c))
22.6b
(sqrt (fma b b (- (* (* (cbrt (* c (* 3.0 a))) (* (cbrt 3.0) (cbrt (* a c)))) (cbrt (* c (* 3.0 a)))))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity
add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
cbrt-prod pow1/3 sqrt-prod
rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 48
Calls
4 calls:
4.0ms
(cbrt (* c (* 3.0 a)))
4.0ms
(cbrt (* c (* 3.0 a)))
1.0ms
(cbrt (* a c))
1.0ms
(sqrt (fma b b (- (* (* (cbrt (* c (* 3.0 a))) (* (cbrt 3.0) (cbrt (* a c)))) (cbrt (* c (* 3.0 a)))))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(cbrt (* c (* 3.0 a)))
94.0ms
(cbrt (* c (* 3.0 a)))
68.0ms
(cbrt (* a c))
135.0ms
(sqrt (fma b b (- (* (* (cbrt (* c (* 3.0 a))) (* (cbrt 3.0) (cbrt (* a c)))) (cbrt (* c (* 3.0 a)))))))

simplify1.3s

Counts
60 → 60
Iterations

Useful iterations: 4 (387.0ms)

IterNodesCost
091879
1181814
2384753
31010738
43407707
done5000707

prune244.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.3b

regimes277.0ms

Accuracy

95.9% (0.9b remaining)

Error of 13.1b against oracle of 12.2b and baseline of 33.9b

bsearch198.0ms

Steps
ItersRangePoint
7
2.703506994090381e+152
2.308573696785045e+154
1.0331115085790278e+154
10
-1.748936198008001e-296
1.7693602656524167e-306
-5.269673295705051e-298
10
-2.699314103090194e+180
-2.227381996671495e+165
-2.272454186637281e+165

simplify11.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04597
16495
28595
39395
done9395

end0.0ms

sample1.1s

Algorithm
intervals
Results
220.0ms5915×body80valid
219.0ms1025×body2560valid
160.0ms893×body1280valid
107.0ms2995×body80nan
63.0ms447×body640valid
30.0ms107×body5120valid
22.0ms210×body320valid
9.0ms103×body160valid