Details

sample178.0ms

Algorithm

intervals

Results

20.0ms	275×	body	80	nan
13.0ms	165×	body	80	valid
8.0ms	29×	body	640	valid
8.0ms	24×	body	1280	valid
6.0ms	21×	body	640	nan
5.0ms	14×	body	1280	nan
5.0ms	23×	body	320	valid
2.0ms	10×	body	320	nan
2.0ms	15×	body	160	valid
1.0ms	6×	body	160	nan

simplify4.0s

Counts

1 → 1

Iterations

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

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.7b

localize56.0ms

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))))
13.7b	(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
23.9b	(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

rewrite226.0ms

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:

100.0ms	(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
59.0ms	(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
16.0ms	(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
38.0ms	(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

710.0ms	(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
746.0ms	(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
306.0ms	(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
490.0ms	(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

simplify1.3s

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
2	2141
1	518
0	216

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.1b

localize44.0ms

Local error

Found 4 expressions with local error:

5.9b	(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
6.2b	(/ (* l l) x)
9.4b	(/ (* t t) x)
29.7b	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

rewrite21.0ms

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:

0.0ms	(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
8.0ms	(/ (* l l) x)
8.0ms	(/ (* t t) x)
3.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
34.0ms	(/ (* l l) x)
35.0ms	(/ (* t t) x)
228.0ms	(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

simplify1.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	2768
1	352
0	131

prune835.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize95.0ms

Local error

Found 4 expressions with local error:

5.9b	(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
29.7b	(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
29.7b	(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
29.7b	(sqrt (* (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))) (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-pow1`
22×	`pow1`
11×	`pow1/2`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow-prod-down` `pow-sqr`
1×	`pow2` `pow-plus` `fma-udef`

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
2.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
2.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
12.0ms	(sqrt (* (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))) (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
246.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
236.0ms	(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
231.0ms	(sqrt (* (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))) (sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))))

simplify1.5s

Counts

78 → 78

Iterations

Iter	Nodes
done	5002
3	2555
2	534
1	187
0	91

prune738.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.1b

localize90.0ms

Local error

Found 4 expressions with local error:

5.9b	(fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t)))
5.9b	(fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t)))
29.7b	(sqrt (fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t))))
29.7b	(sqrt (fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t)))
0.0ms	(fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t)))
1.0ms	(sqrt (fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t))))
1.0ms	(sqrt (fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t))))

series1.4s

Counts

4 → 12

Calls

4 calls:

115.0ms	(fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t)))
122.0ms	(fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t)))
619.0ms	(sqrt (fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t))))
585.0ms	(sqrt (fma 2.0 (fma l (/ l x) (* t t)) (/ 4.0 (/ (/ x t) t))))

simplify1.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	2276
2	424
1	133
0	64

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.1b

regimes732.0ms

Accuracy

76.5% (5.5b remaining)

Error of 9.7b against oracle of 4.2b and baseline of 27.7b

bsearch1.0s

Steps

Iters	Range		Point
9	2.3682169563964882e+42	1.376222274811364e+49	5.469601309486937e+45
8	1.7412922778296343e-165	2.5725953662274735e-162	6.783164823431965e-165
11	9.485480553618113e-206	2.7798908565106377e-186	3.4247796977069794e-203
10	-2.3531295468621075e+92	-8.259027920981738e+77	-5.354437256926886e+88

simplify24.0ms

Iterations

Iter	Nodes
done	71
3	71
2	68
1	62
0	51

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.4s	10170×	body	80	nan
1.1s	5053×	body	80	valid
903.0ms	1029×	body	640	valid
575.0ms	875×	body	1280	valid
384.0ms	571×	body	1280	nan
301.0ms	579×	body	640	nan
298.0ms	663×	body	320	valid
173.0ms	336×	body	320	nan
90.0ms	223×	body	160	nan
74.0ms	380×	body	160	valid