Details

sample343.0ms

Algorithm

intervals

Results

55.0ms	338×	body	80	nan
54.0ms	7×	body	320	nan
25.0ms	161×	body	80	valid
25.0ms	34×	body	1280	valid
18.0ms	29×	body	640	valid
10.0ms	16×	body	640	nan
9.0ms	12×	body	1280	nan
9.0ms	20×	body	320	valid
4.0ms	12×	body	160	valid
1.0ms	5×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	2403
5	990
4	463
3	210
2	99
1	42
0	18

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.1b

localize46.0ms

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))))
0.4b	(* (sqrt 2) t)
12.7b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
19.3b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite237.0ms

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:

87.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2) t)
53.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
78.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

433.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
67.0ms	(* (sqrt 2) t)
249.0ms	(- (* (/ (+ 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)))

simplify11.3s

Counts

106 → 106

Iterations

Iter	Nodes
3	7341
2	1684
1	466
0	181

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
3.6b	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
8.8b	(/ (* t (* 4 t)) x)
26.0b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite53.0ms

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:

14.0ms	(* (sqrt 2) t)
0.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
34.0ms	(/ (* t (* 4 t)) x)
2.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sqrt 2) t)
95.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
47.0ms	(/ (* t (* 4 t)) x)
347.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

simplify3.1s

Counts

90 → 90

Iterations

Iter	Nodes
3	4978
2	1093
1	338
0	147

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
3.6b	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
8.8b	(/ (* t (* 4 t)) x)
26.0b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite64.0ms

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:

43.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
18.0ms	(/ (* t (* 4 t)) x)
1.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
78.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
36.0ms	(/ (* t (* 4 t)) x)
386.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

simplify2.8s

Counts

92 → 92

Iterations

Iter	Nodes
3	5273
2	1212
1	369
0	153

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (cbrt (sqrt 2))) (* (sqrt (sqrt 2)) t))
3.6b	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
8.8b	(/ (* t (* 4 t)) x)
26.0b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
15×	`sqrt-prod`
12×	`add-sqr-sqrt` `associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
6×	`cbrt-prod` `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 → 83

Calls

4 calls:

42.0ms	(* (sqrt (cbrt (sqrt 2))) (* (sqrt (sqrt 2)) t))
0.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
17.0ms	(/ (* t (* 4 t)) x)
8.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

536.0ms	(* (sqrt (cbrt (sqrt 2))) (* (sqrt (sqrt 2)) t))
121.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
40.0ms	(/ (* t (* 4 t)) x)
394.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

simplify3.1s

Counts

95 → 95

Iterations

Iter	Nodes
3	6159
2	1301
1	399
0	167

prune1.9s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.0b

regimes734.0ms

Accuracy

78.1% (5.1b remaining)

Error of 8.9b against oracle of 3.8b and baseline of 27.0b

bsearch1.5s

Steps

Iters	Range		Point
8	7.917799159621275e+106	2.002559075649937e+110	1.4994412213892464e+108
10	2.313298500987685e-178	3.946360535693021e-163	3.464075321521421e-166
8	4.923607766514643e-262	1.9892195058960085e-259	8.264925603641206e-260
9	-8.613554016052439e+67	-7.040451668859043e+60	-2.3433794278040432e+67

simplify28.0ms

Iterations

Iter	Nodes
2	65
1	65
0	54

end0.0ms

sample9.1s

Algorithm

intervals

Results

2.6s	10039×	body	80	nan
1.3s	5077×	body	80	valid
1.1s	620×	body	1280	nan
974.0ms	861×	body	1280	valid
922.0ms	1042×	body	640	valid
594.0ms	612×	body	640	nan
501.0ms	665×	body	320	valid
200.0ms	353×	body	320	nan
196.0ms	355×	body	160	valid
69.0ms	186×	body	160	nan