Details

sample307.0ms

Algorithm

intervals

Results

68.0ms	24×	body	1280	valid
34.0ms	341×	body	80	nan
19.0ms	168×	body	80	valid
14.0ms	35×	body	640	valid
8.0ms	23×	body	640	nan
6.0ms	14×	body	1280	nan
6.0ms	23×	body	320	valid
1.0ms	5×	body	320	nan
1.0ms	6×	body	160	valid
0.0ms	3×	body	160	nan

simplify6.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5010
7	2894
6	1606
5	890
4	445
3	209
2	98
1	41
0	18

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize89.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
11.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite242.0ms

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:

80.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
14.0ms	(* (sqrt 2.0) t)
60.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
82.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series4.1s

Counts

4 → 12

Calls

4 calls:

923.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
73.0ms	(* (sqrt 2.0) t)
534.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.6s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify3.6s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1721
1	476
0	182

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.1b

localize114.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
3.2b	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
9.0b	(/ (* 4.0 (* t t)) x)
26.7b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `times-frac` `div-exp` `associate-r*`
2×	`unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 78

Calls

4 calls:

24.0ms	(* (sqrt 2.0) t)
1.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
26.0ms	(/ (* 4.0 (* t t)) x)
4.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

series764.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sqrt 2.0) t)
139.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
37.0ms	(/ (* 4.0 (* t t)) x)
522.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

simplify2.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1236
1	354
0	146

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

localize128.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.2b	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
9.0b	(/ (* 4.0 (* t t)) x)
26.7b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

95.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
2.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
41.0ms	(/ (* 4.0 (* t t)) x)
6.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

series825.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
148.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
64.0ms	(/ (* 4.0 (* t t)) x)
533.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

simplify3.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1466
1	396
0	152

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
3.2b	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
9.0b	(/ (* 4.0 (* t t)) x)
26.7b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

71.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
1.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
30.0ms	(/ (* 4.0 (* t t)) x)
3.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

series818.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
143.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
36.0ms	(/ (* 4.0 (* t t)) x)
572.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

simplify3.5s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1350
1	383
0	153

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.0b

regimes1.6s

Accuracy

77.2% (5.3b remaining)

Error of 9.0b against oracle of 3.7b and baseline of 27.0b

bsearch365.0ms

Steps

Iters	Range		Point
8	2.0215799830271626e+96	1.863612731888614e+99	1.4235245726759946e+99
7	-8.62882115661326e+99	-1.9133687329772835e+98	-6.629018353342802e+99

simplify43.0ms

Iterations

Iter	Nodes
done	52
1	52
0	45

end0.0ms

sample6.2s

Algorithm

intervals

Results

1.3s	10091×	body	80	nan
1.2s	5042×	body	80	valid
553.0ms	1038×	body	640	valid
544.0ms	356×	body	160	valid
488.0ms	903×	body	1280	valid
351.0ms	607×	body	1280	nan
293.0ms	661×	body	320	valid
244.0ms	627×	body	640	nan
195.0ms	335×	body	320	nan
82.0ms	186×	body	160	nan