Details

sample522.0ms

Algorithm

intervals

Results

125.0ms	39×	body	1280	valid
60.0ms	277×	body	80	nan
49.0ms	14×	body	1280	nan
31.0ms	37×	body	640	valid
30.0ms	140×	body	80	valid
18.0ms	28×	body	320	valid
12.0ms	14×	body	640	nan
7.0ms	11×	body	320	nan
5.0ms	12×	body	160	valid
2.0ms	5×	body	160	nan

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	2257
5	970
4	472
3	215
2	101
1	44
0	18

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.8b

localize47.0ms

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)
16.7b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
17.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite146.0ms

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:

69.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2) t)
25.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
42.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

497.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
50.0ms	(* (sqrt 2) t)
266.0ms	(- (* (/ (+ 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)))

simplify6.1s

Counts

106 → 106

Iterations

Iter	Nodes
3	8091
2	1703
1	467
0	181

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize67.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t))))
9.2b	(/ (* l l) x)
9.3b	(/ x (* t t))
26.6b	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

9.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t))))
18.0ms	(/ (* l l) x)
14.0ms	(/ x (* t t))
3.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t)))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t))))
21.0ms	(/ (* l l) x)
31.0ms	(/ x (* t t))
365.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t)))))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
3	3099
2	889
1	300
0	135

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ l (/ x l))
0.4b	(* (sqrt 2) t)
0.8b	(fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2)))
26.6b	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

11.0ms	(/ l (/ x l))
14.0ms	(* (sqrt 2) t)
0.0ms	(fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2)))
2.0ms	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ l (/ x l))
70.0ms	(* (sqrt 2) t)
98.0ms	(fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2)))
463.0ms	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2))))

simplify2.5s

Counts

137 → 137

Iterations

Iter	Nodes
3	5085
2	1532
1	534
0	237

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.3b	(* (sqrt (sqrt 2)) t)
0.8b	(fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2)))
26.6b	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
19×	`add-sqr-sqrt`
18×	`associate-l`
12×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 83

Calls

4 calls:

47.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
10.0ms	(* (sqrt (sqrt 2)) t)
0.0ms	(fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2)))
1.0ms	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
140.0ms	(* (sqrt (sqrt 2)) t)
76.0ms	(fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2)))
471.0ms	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ (/ 4 x) 2))))

simplify860.0ms

Counts

95 → 95

Iterations

Iter	Nodes
3	2392
2	726
1	273
0	124

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

regimes621.0ms

Accuracy

78.1% (5.2b remaining)

Error of 9.2b against oracle of 4.0b and baseline of 27.5b

bsearch1.2s

Steps

Iters	Range		Point
9	1.3356406669163853e+121	2.4586850594315566e+126	3.7543841451851774e+122
9	5.484666736935185e-166	2.0396808824752205e-160	5.72877141657189e-164
10	1.1525372111554329e-223	4.636776026529116e-210	3.622605389449186e-213
6	-6.778571632960239e+103	-9.951417039093262e+102	-1.9501808158464715e+103

simplify41.0ms

Iterations

Iter	Nodes
4	62
3	62
2	59
1	56
0	46

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.5s	10002×	body	80	nan
1.6s	5128×	body	80	valid
854.0ms	1009×	body	640	valid
842.0ms	863×	body	1280	valid
800.0ms	641×	body	320	valid
558.0ms	549×	body	1280	nan
486.0ms	608×	body	640	nan
209.0ms	351×	body	320	nan
143.0ms	359×	body	160	valid
58.0ms	182×	body	160	nan