Details

Time bar (total: 7.0s)

sample39.0ms

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

simplify45.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12117
24116
37616
49016
59816
done9816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
add-exp-log add-cbrt-cube
*-un-lft-identity add-log-exp
add-cube-cbrt
sqrt-prod
flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
sub-neg sqrt-div diff-log difference-of-squares
rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
6.0ms
(* (* 3.0 a) c)
2.0ms
(- (* b b) (* (* 3.0 a) c))
18.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
43.0ms
(- (* b b) (* (* 3.0 a) c))
77.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify466.0ms

Counts
72 → 72
Iterations

Useful iterations: done (464.0ms)

IterNodesCost
01201001
1283903
21077825
done5000821

prune186.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 3.0 (* a c))
1.0b
(- (pow b 2) (* 3.0 (* a c)))
1.4b
(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
22.6b
(sqrt (- (pow b 2) (* 3.0 (* a c))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
add-exp-log add-cbrt-cube
*-un-lft-identity add-log-exp
add-cube-cbrt
sqrt-prod
flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod
sub-neg sqrt-div diff-log difference-of-squares
rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
6.0ms
(* 3.0 (* a c))
7.0ms
(- (pow b 2) (* 3.0 (* a c)))
37.0ms
(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
8.0ms
(sqrt (- (pow b 2) (* 3.0 (* a c))))

series211.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* 3.0 (* a c))
45.0ms
(- (pow b 2) (* 3.0 (* a c)))
76.0ms
(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
69.0ms
(sqrt (- (pow b 2) (* 3.0 (* a c))))

simplify1.2s

Counts
72 → 72
Iterations

Useful iterations: 3 (295.0ms)

IterNodesCost
0116998
1266894
2828828
33103820
done5000820

prune176.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.4b

localize18.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (* 3.0 (* a c)))
15.3b
(cbrt (* 3.0 (* a c)))
15.3b
(cbrt (* 3.0 (* a c)))
22.6b
(sqrt (- (pow b 2) (* (* (cbrt (* 3.0 (* a c))) (cbrt (* 3.0 (* a c)))) (cbrt (* 3.0 (* a c))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity
add-exp-log add-cbrt-cube add-log-exp
cbrt-prod pow1/3 sqrt-prod
sqrt-div
rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 42
Calls
4 calls:
4.0ms
(cbrt (* 3.0 (* a c)))
4.0ms
(cbrt (* 3.0 (* a c)))
4.0ms
(cbrt (* 3.0 (* a c)))
7.0ms
(sqrt (- (pow b 2) (* (* (cbrt (* 3.0 (* a c))) (cbrt (* 3.0 (* a c)))) (cbrt (* 3.0 (* a c))))))

series409.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (* 3.0 (* a c)))
94.0ms
(cbrt (* 3.0 (* a c)))
95.0ms
(cbrt (* 3.0 (* a c)))
123.0ms
(sqrt (- (pow b 2) (* (* (cbrt (* 3.0 (* a c))) (cbrt (* 3.0 (* a c)))) (cbrt (* 3.0 (* a c))))))

simplify794.0ms

Counts
54 → 54
Iterations

Useful iterations: done (792.0ms)

IterNodesCost
085981
1199889
2513531
31907520
done5001513

prune194.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.4b

localize19.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (* 3.0 (* a c)))
15.3b
(cbrt (* 3.0 (* a c)))
15.3b
(cbrt (* a c))
22.6b
(sqrt (- (pow b 2) (* (* (cbrt (* 3.0 (* a c))) (* (cbrt 3.0) (cbrt (* a c)))) (cbrt (* 3.0 (* a c))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity
add-exp-log add-cbrt-cube add-log-exp
cbrt-prod pow1/3 sqrt-prod
sqrt-div
rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 42
Calls
4 calls:
4.0ms
(cbrt (* 3.0 (* a c)))
4.0ms
(cbrt (* 3.0 (* a c)))
1.0ms
(cbrt (* a c))
7.0ms
(sqrt (- (pow b 2) (* (* (cbrt (* 3.0 (* a c))) (* (cbrt 3.0) (cbrt (* a c)))) (cbrt (* 3.0 (* a c))))))

series379.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (* 3.0 (* a c)))
94.0ms
(cbrt (* 3.0 (* a c)))
66.0ms
(cbrt (* a c))
122.0ms
(sqrt (- (pow b 2) (* (* (cbrt (* 3.0 (* a c))) (* (cbrt 3.0) (cbrt (* a c)))) (cbrt (* 3.0 (* a c))))))

simplify890.0ms

Counts
54 → 54
Iterations

Useful iterations: done (888.0ms)

IterNodesCost
097973
1217878
2573809
32355774
done5001767

prune218.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.4b

regimes217.0ms

Accuracy

84.7% (3.3b remaining)

Error of 15.6b against oracle of 12.2b and baseline of 33.9b

bsearch128.0ms

Steps
ItersRangePoint
9
2.358314391323758e-60
7.760624497279612e-54
3.5034007549662594e-57
10
-2.699314103090194e+180
-2.227381996671495e+165
-2.272454186637281e+165

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03466
14266
done4266

end0.0ms

sample1.1s

Algorithm
intervals
Results
223.0ms1025×body2560valid
217.0ms5915×body80valid
155.0ms893×body1280valid
102.0ms2995×body80nan
62.0ms447×body640valid
29.0ms107×body5120valid
23.0ms210×body320valid
7.0ms103×body160valid