Details

Time bar (total: 18.8s)

sample70.0ms

Algorithm
intervals
Results
14.0ms38×body2560valid
11.0ms178×body80valid
10.0ms29×body1280valid
5.0ms79×body80nan
3.0ms10×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify119.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01217
12217
24216
38216
410416
511216
done11216

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.6b
(- (* b b) (* (* 3.0 a) c))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff
16×sqrt-prod
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
21.0ms
(* (* 3.0 a) c)
71.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
9.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (* 3.0 a) c)
108.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
61.0ms
(- (* b b) (* (* 3.0 a) c))
114.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.9s

Counts
106 → 106
Iterations

Useful iterations: 3 (2.1s)

IterNodesCost
01611863
13671562
211281333
345011245
done50001245

prune410.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 3.0 a) c))
0.6b
(- (* b b) (* (* 3.0 a) c))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
9.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* b b) (* (* 3.0 a) c))
60.0ms
(- (* b b) (* (* 3.0 a) c))
110.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.5s

Counts
78 → 78
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0711146
11681050
2574952
32407952
done5000936

prune454.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.3b

localize44.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
23.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
116.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
141.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.9s

Counts
80 → 80
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0541228
11391080
24471004
317101004
done50011000

prune537.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.6b
(- (* b b) (* (* 3.0 a) c))
20.0b
(cbrt (pow (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
28×*-un-lft-identity
22×add-cube-cbrt
19×prod-diff
18×cbrt-prod sqrt-prod
8×add-log-exp
7×fma-neg
6×unpow-prod-down cube-prod difference-of-squares
5×pow1
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×distribute-lft-out--
2×cube-div sub-neg cbrt-div sqrt-div diff-log
1×cube-mult rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 105
Calls
4 calls:
88.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
18.0ms
(- (* b b) (* (* 3.0 a) c))
52.0ms
(cbrt (pow (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3))
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
87.0ms
(- (* b b) (* (* 3.0 a) c))
139.0ms
(cbrt (pow (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3))
99.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts
117 → 117
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01692598
13882096
211391851
done50011766

prune460.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 10.3b

regimes299.0ms

Accuracy

86.8% (2.9b remaining)

Error of 15.4b against oracle of 12.5b and baseline of 34.3b

bsearch145.0ms

Steps
ItersRangePoint
8
4.924640387312937e-45
5.473977791176249e-42
4.102989996811912e-44
9
-4.4874797001979404e+160
-1.588602326591779e+153
-1.3506760573432116e+154

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02749
13249
done3249

end0.0ms

sample3.7s

Algorithm
intervals
Results
982.0ms5807×body80valid
774.0ms2994×body80nan
588.0ms1087×body2560valid
407.0ms931×body1280valid
140.0ms447×body640valid
110.0ms117×body5120valid
79.0ms114×body160valid
42.0ms209×body320valid