Details

Time bar (total: 20.6s)

sample94.0ms

Algorithm
intervals
Results
17.0ms4×body160valid
17.0ms188×body80valid
17.0ms35×body2560valid
10.0ms28×body1280valid
6.0ms85×body80nan
4.0ms14×body640valid
4.0ms5×body5120valid
2.0ms10×body320valid

simplify99.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
377
244
125
014

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
1.0b
(fma b b (* (* a -4) c))
1.6b
(- (sqrt (fma b b (* (* a -4) c))) b)
21.2b
(sqrt (fma b b (* (* a -4) c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
51.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms
(fma b b (* (* a -4) c))
20.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
3.0ms
(sqrt (fma b b (* (* a -4) c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
55.0ms
(fma b b (* (* a -4) c))
92.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
122.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify2.5s

Counts
126 → 126
Iterations
IterNodes
done5000
33845
21007
1423
0180

prune679.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
1.0b
(fma b b (* (* a -4) c))
1.6b
(- (sqrt (fma b b (* (* a -4) c))) b)
21.2b
(sqrt (fma b b (* (* a -4) c)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- flip-- unswap-sqr
2×frac-times div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef div-inv
Counts
4 → 115
Calls
4 calls:
83.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
1.0ms
(fma b b (* (* a -4) c))
22.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
4.0ms
(sqrt (fma b b (* (* a -4) c)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
80.0ms
(fma b b (* (* a -4) c))
120.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
97.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify2.6s

Counts
127 → 127
Iterations
IterNodes
done5000
34101
21224
1485
0200

prune630.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize27.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (fma b b (* (* a -4) c))) b)
1.6b
(- (sqrt (fma b b (* (* a -4) c))) b)
21.2b
(sqrt (fma b b (* (* a -4) c)))
21.2b
(sqrt (fma b b (* (* a -4) c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
17.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
15.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms
(sqrt (fma b b (* (* a -4) c)))
9.0ms
(sqrt (fma b b (* (* a -4) c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
132.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
107.0ms
(sqrt (fma b b (* (* a -4) c)))
90.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify3.5s

Counts
128 → 128
Iterations
IterNodes
done5000
44883
31446
2484
1225
0100

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
1.0b
(fma b b (* (* a -4) c))
1.6b
(- (sqrt (fma b b (* (* a -4) c))) b)
21.2b
(sqrt (fma b b (* (* a -4) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
6×fma-neg add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-prod
2×difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 pow1/3 diff-log fma-udef flip-- distribute-lft-out--
Counts
4 → 83
Calls
4 calls:
1.0ms
(cbrt a)
0.0ms
(fma b b (* (* a -4) c))
22.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
3.0ms
(sqrt (fma b b (* (* a -4) c)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(cbrt a)
62.0ms
(fma b b (* (* a -4) c))
112.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
116.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify2.7s

Counts
95 → 95
Iterations
IterNodes
done5001
32091
2651
1282
0135

prune532.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.6b

regimes571.0ms

Accuracy

86.1% (3.8b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 32.5b

bsearch290.0ms

Steps
ItersRangePoint
7
3.170449429657488e+21
2.218413533118306e+23
1.1597179970514171e+23
9
5.111551936031541e-102
3.986693767760393e-93
5.4213851798811764e-102
6
-2.971125736392027e+46
-1.937449214055594e+45
-2.900769547116861e+46

simplify8.0ms

Iterations
IterNodes
done49
149
042

end0.0ms

sample3.0s

Algorithm
intervals
Results
665.0ms2988×body80nan
632.0ms1083×body2560valid
575.0ms5804×body80valid
481.0ms932×body1280valid
210.0ms489×body640valid
54.0ms107×body5120valid
54.0ms247×body320valid
17.0ms121×body160valid