Details

sample84.0ms

Algorithm

intervals

Results

15.0ms	302×	body	80	nan
11.0ms	22×	body	1280	nan
9.0ms	36×	body	1280	valid
8.0ms	160×	body	80	valid
5.0ms	26×	body	640	valid
3.0ms	21×	body	320	valid
3.0ms	17×	body	640	nan
2.0ms	14×	body	320	nan
1.0ms	13×	body	160	valid
1.0ms	9×	body	160	nan

simplify93.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	14
1	101	14
2	234	14
3	525	14
4	1016	14
5	1701	14
6	3626	14
7	5002	14
done	5002	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 47.0b

localize18.0ms

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)
14.5b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

55.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms	(* (sqrt 2.0) t)
30.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
51.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

445.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms	(* (sqrt 2.0) t)
228.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify62.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	446	1290
1	2206	1177
2	5002	1172
done	5002	1172

prune342.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.3b	(/ (pow l 2) x)
12.7b	(/ (pow t 2) x)
31.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
8.0ms	(/ (pow l 2) x)
8.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow l 2) x)
24.0ms	(/ (pow t 2) x)
267.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify46.0ms

Counts

139 → 139

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	377	837
1	1450	724
2	5001	715
done	5001	715

prune480.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
3.2b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
12.7b	(/ (pow t 2) x)
31.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

10.0ms	(* (sqrt 2.0) t)
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
8.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt 2.0) t)
72.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow t 2) x)
268.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify41.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	325	681
1	1256	616
2	5002	609
done	5002	609

prune403.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
3.2b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
12.7b	(/ (pow t 2) x)
31.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
14×	`add-exp-log`
12×	`unpow-prod-down` `sqrt-prod`
11×	`add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `pow-exp` `clear-num` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

36.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
8.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
73.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow t 2) x)
271.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify45.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	362	761
1	1328	665
2	5002	653
done	5002	653

prune419.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.3b

regimes281.0ms

Accuracy

76.9% (5.5b remaining)

Error of 9.5b against oracle of 4.0b and baseline of 27.7b

bsearch172.0ms

Steps

Iters	Range		Point
6	1.2840148601205861e+123	1.0171677682422529e+124	1.5846168501932176e+123
9	-4.503098316815935e+50	-1.4718051122419779e+43	-4.4121797185245335e+50

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	53
1	56	53
done	56	53

end0.0ms

sample2.2s

Algorithm

intervals

Results

468.0ms	9981×	body	80	nan
254.0ms	5103×	body	80	valid
212.0ms	870×	body	1280	valid
187.0ms	1004×	body	640	valid
142.0ms	619×	body	1280	nan
105.0ms	582×	body	640	nan
98.0ms	659×	body	320	valid
48.0ms	361×	body	320	nan
36.0ms	364×	body	160	valid
18.0ms	189×	body	160	nan