Details

sample516.0ms

Algorithm

intervals

Results

133.0ms	156×	body	80	valid
67.0ms	300×	body	80	nan
57.0ms	45×	body	640	valid
15.0ms	26×	body	1280	valid
10.0ms	16×	body	1280	nan
7.0ms	17×	body	320	valid
6.0ms	13×	body	640	nan
3.0ms	10×	body	320	nan
3.0ms	12×	body	160	valid
2.0ms	10×	body	160	nan

simplify4.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4703
6	1985
5	1092
4	526
3	232
2	100
1	41
0	18

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
0.3b	(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
14.2b	(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
19.1b	(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
76×	`times-frac`
74×	`add-sqr-sqrt`
59×	`*-un-lft-identity` `add-cube-cbrt`
42×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `sqrt-div` `associate-/l` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--`
3×	`associate-l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 164

Calls

4 calls:

102.0ms	(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
66.0ms	(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
31.0ms	(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
49.0ms	(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

series2.1s

Counts

4 → 12

Calls

4 calls:

644.0ms	(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
703.0ms	(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
293.0ms	(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
445.0ms	(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

simplify1.1s

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
2	2141
1	518
0	216

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 28.8b

localize58.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
7.4b	(/ (* l l) x)
8.1b	(/ (* t t) x)
27.7b	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 71

Calls

4 calls:

1.0ms	(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
15.0ms	(/ (* l l) x)
16.0ms	(/ (* t t) x)
3.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
20.0ms	(/ (* l l) x)
27.0ms	(/ (* t t) x)
236.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

simplify1.4s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	2768
1	352
0	131

prune620.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt 2.0) (sqrt (fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0))))))
5.3b	(fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0))))
8.1b	(/ (* t t) (/ x 4.0))
27.7b	(sqrt (fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
19×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-undiv` `sqrt-pow1` `pow1/2` `associate-/r/` `fma-udef`

Counts

4 → 136

Calls

4 calls:

13.0ms	(/ (sqrt 2.0) (sqrt (fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0))))))
1.0ms	(fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0))))
18.0ms	(/ (* t t) (/ x 4.0))
1.0ms	(sqrt (fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0)))))

series827.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(/ (sqrt 2.0) (sqrt (fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0))))))
99.0ms	(fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0))))
31.0ms	(/ (* t t) (/ x 4.0))
379.0ms	(sqrt (fma (* 2.0 t) t (fma (/ l (/ x l)) 2.0 (/ (* t t) (/ x 4.0)))))

simplify1.9s

Counts

148 → 148

Iterations

Iter	Nodes
done	5001
2	3182
1	551
0	238

prune938.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (/ (cbrt (sqrt 2.0)) (sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x))))))
4.2b	(fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x)))
8.4b	(/ (* (* t t) 4.0) x)
27.7b	(sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
58×	`add-sqr-sqrt` `associate-r`
53×	`sqrt-prod`
44×	`*-un-lft-identity` `add-cube-cbrt`
40×	`cbrt-prod`
25×	`add-exp-log`
19×	`add-cbrt-cube`
10×	`pow1`
9×	`prod-exp` `cbrt-unprod`
7×	`unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `pow-prod-down`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `associate-r/` `-commutative` `fma-udef` `associate-/l*`

Counts

4 → 137

Calls

4 calls:

98.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (/ (cbrt (sqrt 2.0)) (sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x))))))
1.0ms	(fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x)))
21.0ms	(/ (* (* t t) 4.0) x)
1.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x))))

series804.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (/ (cbrt (sqrt 2.0)) (sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x))))))
104.0ms	(fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x)))
52.0ms	(/ (* (* t t) 4.0) x)
368.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (/ (* (* t t) 4.0) x))))

simplify385.0ms

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
1	736
0	250

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.4b

regimes1.4s

Accuracy

75.5% (5.9b remaining)

Error of 9.9b against oracle of 4.0b and baseline of 28.1b

bsearch561.0ms

Steps

Iters	Range		Point
4	1.4336744111234639e+149	2.696708458502892e+149	1.8145802542560214e+149
9	6.906315603593477e-164	9.191228058584716e-159	2.0849622643324037e-159
5	1.8889114741052636e-285	4.82560000307667e-285	3.654137014915323e-285
2	-6.116329696038052e+95	-5.398717659021071e+95	-5.488419163648194e+95

simplify7.0ms

Iterations

Iter	Nodes
done	66
1	66
0	56

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.2s	10078×	body	80	nan
935.0ms	902×	body	1280	valid
641.0ms	5111×	body	80	valid
592.0ms	980×	body	640	valid
335.0ms	597×	body	1280	nan
281.0ms	652×	body	320	valid
272.0ms	568×	body	640	nan
101.0ms	334×	body	320	nan
71.0ms	355×	body	160	valid
36.0ms	184×	body	160	nan