Details

Time bar (total: 11.1s)

sample39.0ms

Algorithm
intervals
Results
7.0ms206×body80valid
5.0ms27×body2560valid
4.0ms29×body1280valid
4.0ms105×body80nan
2.0ms13×body640valid
0.0ms2×body5120valid
0.0ms6×body160valid
0.0ms4×body320valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01217
12217
24216
38216
410416
511216
done11216

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
1.0b
(- (* b b) (* (* 3.0 a) c))
1.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
95.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
11.0ms
(- (* b b) (* (* 3.0 a) c))
51.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
46.0ms
(- (* b b) (* (* 3.0 a) c))
82.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
75.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify977.0ms

Counts
118 → 118
Iterations

Useful iterations: done (974.0ms)

IterNodesCost
01952476
14752171
214161863
done50001791

prune283.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* 3.0 a))
1.0b
(- (* b b) (* (* 3.0 a) c))
1.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
16×sqrt-prod
15×add-exp-log
9×add-cbrt-cube
8×pow1 add-log-exp
7×fma-neg
4×expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- times-frac prod-exp flip-- associate-/l*
2×cbrt-undiv sub-neg rec-exp pow-flip sqrt-div diff-log 1-exp difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* cbrt-unprod div-inv distribute-lft-out-- inv-pow
Counts
4 → 104
Calls
4 calls:
13.0ms
(/ 1 (* 3.0 a))
9.0ms
(- (* b b) (* (* 3.0 a) c))
51.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ 1 (* 3.0 a))
48.0ms
(- (* b b) (* (* 3.0 a) c))
81.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts
116 → 116
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01781913
13931589
210861358
344451271
done50001271

prune247.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)))
1.0b
(- (* b b) (* (* 3.0 a) c))
1.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 152
Calls
4 calls:
61.0ms
(/ 1 (/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)))
9.0ms
(- (* b b) (* (* 3.0 a) c))
54.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ 1 (/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)))
46.0ms
(- (* b b) (* (* 3.0 a) c))
84.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
75.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify957.0ms

Counts
164 → 164
Iterations

Useful iterations: done (949.0ms)

IterNodesCost
02604025
15833484
216373082
done50002938

prune312.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.2b

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)))
1.2b
(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
21.1b
(sqrt (- (pow b 2) (* 3.0 (* a c))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
26×*-un-lft-identity prod-diff
24×add-cube-cbrt
16×sqrt-prod
14×fma-neg
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×unpow-prod-down
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log unpow2 difference-of-squares sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 108
Calls
4 calls:
16.0ms
(* 3.0 (* a c))
19.0ms
(- (pow b 2) (* 3.0 (* a c)))
85.0ms
(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
18.0ms
(sqrt (- (pow b 2) (* 3.0 (* a c))))

series225.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* 3.0 (* a c))
47.0ms
(- (pow b 2) (* 3.0 (* a c)))
83.0ms
(- (sqrt (- (pow b 2) (* 3.0 (* a c)))) b)
75.0ms
(sqrt (- (pow b 2) (* 3.0 (* a c))))

simplify2.4s

Counts
120 → 120
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01732088
13951768
210401508
346601409
done50001409

prune290.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.2b

regimes354.0ms

Accuracy

78.6% (6.0b remaining)

Error of 11.5b against oracle of 5.4b and baseline of 33.6b

bsearch168.0ms

Steps
ItersRangePoint
8
0.0001820196720056695
0.3848154462067827
0.00018465375781150442
6
3.6410892437809104e-110
3.0960233903298005e-109
6.194358139220984e-110
8
1.0691773024250323e-170
5.5548132533506025e-168
5.480131987291899e-168
5
-1.2890659370140747e+99
-5.778998546738359e+98
-1.26989575591942e+99

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03984
15180
done5180

end0.0ms

sample1.1s

Algorithm
intervals
Results
211.0ms1041×body2560valid
202.0ms5926×body80valid
147.0ms905×body1280valid
103.0ms2854×body80nan
58.0ms464×body640valid
25.0ms102×body5120valid
21.0ms225×body320valid
6.0ms94×body160valid