Details

sample290.0ms

Algorithm

intervals

Results

30.0ms	341×	body	80	nan
18.0ms	168×	body	80	valid
12.0ms	35×	body	640	valid
11.0ms	24×	body	1280	valid
8.0ms	23×	body	640	nan
6.0ms	23×	body	320	valid
5.0ms	14×	body	1280	nan
1.0ms	5×	body	320	nan
1.0ms	6×	body	160	valid
0.0ms	3×	body	160	nan

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4592
5	1370
4	472
3	215
2	101
1	44
0	18

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.7b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.5b	(* (sqrt 2) t)
11.9b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.3b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 94

Calls

4 calls:

91.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
20.0ms	(* (sqrt 2) t)
49.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
89.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.4s

Counts

4 → 12

Calls

4 calls:

469.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
75.0ms	(* (sqrt 2) t)
306.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify2.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1605
1	483
0	181

prune761.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.3b

localize36.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
5.9b	(/ (* l l) x)
8.8b	(/ (* t t) x)
26.7b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

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` `insert-posit16` `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 → 75

Calls

4 calls:

1.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
21.0ms	(/ (* l l) x)
12.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
35.0ms	(/ (* l l) x)
34.0ms	(/ (* t t) x)
201.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

simplify1.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	5020
2	1498
1	356
0	134

prune569.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
3.2b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2)))
8.8b	(/ (* t t) x)
26.7b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt x)
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2)))
10.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(cbrt x)
121.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2)))
31.0ms	(/ (* t t) x)
246.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

simplify1.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	5029
2	1071
1	298
0	124

prune605.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize105.0ms

Local error

Found 4 expressions with local error:

8.8b	(/ (* t t) x)
8.8b	(/ (* t t) x)
26.7b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))
26.7b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `associate-/r*` `times-frac` `sqrt-prod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

11.0ms	(/ (* t t) x)
12.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))
2.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* t t) x)
26.0ms	(/ (* t t) x)
248.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))
216.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

simplify1.5s

Counts

92 → 92

Iterations

Iter	Nodes
done	5004
2	846
1	224
0	88

prune760.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.1b

regimes774.0ms

Accuracy

77.2% (5.3b remaining)

Error of 9.0b against oracle of 3.7b and baseline of 26.8b

bsearch317.0ms

Steps

Iters	Range		Point
8	2.0215799830271626e+96	1.863612731888614e+99	1.4235245726759946e+99
7	-8.62882115661326e+99	-1.9133687329772835e+98	-3.6519455046374026e+98

simplify17.0ms

Iterations

Iter	Nodes
done	46
1	46
0	42

end0.0ms

sample6.0s

Algorithm

intervals

Results

1.2s	10091×	body	80	nan
1.0s	5042×	body	80	valid
816.0ms	607×	body	1280	nan
773.0ms	627×	body	640	nan
504.0ms	903×	body	1280	valid
463.0ms	1038×	body	640	valid
367.0ms	661×	body	320	valid
128.0ms	356×	body	160	valid
110.0ms	186×	body	160	nan
101.0ms	335×	body	320	nan