Details

sample88.0ms

Algorithm

intervals

Results

25.0ms	340×	body	80	nan
8.0ms	161×	body	80	valid
8.0ms	29×	body	1280	valid
6.0ms	32×	body	640	valid
5.0ms	21×	body	1280	nan
5.0ms	27×	body	640	nan
3.0ms	23×	body	320	valid
2.0ms	14×	body	320	nan
1.0ms	11×	body	160	valid
0.0ms	4×	body	160	nan

simplify95.0ms

Algorithm

egg-herbie

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

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)
13.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite56.0ms

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:

18.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
14.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
16.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

430.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
46.0ms	(* (sqrt 2.0) t)
218.0ms	(- (* (/ (+ 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)))

simplify64.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (51.0ms)

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

prune360.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.8b

localize17.0ms

Local error

Found 4 expressions with local error:

4.2b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.2b	(/ (pow l 2) x)
9.9b	(/ (pow t 2) x)
27.6b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite17.0ms

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:

1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (pow l 2) x)
5.0ms	(/ (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)))))

series373.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow l 2) x)
23.0ms	(/ (pow t 2) x)
265.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (33.0ms)

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

prune482.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
4.2b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.9b	(/ (pow t 2) x)
27.6b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

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:

5.0ms	(* (sqrt 2.0) t)
1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (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)))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt 2.0) t)
64.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
24.0ms	(/ (pow t 2) x)
267.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (34.0ms)

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

prune436.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
4.2b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.9b	(/ (pow t 2) x)
27.6b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

11.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (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)))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
64.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
20.0ms	(/ (pow t 2) x)
275.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	375	871
1	1418	715
2	5002	664

prune401.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.7b

regimes548.0ms

Accuracy

76% (5.7b remaining)

Error of 9.7b against oracle of 3.9b and baseline of 27.8b

bsearch159.0ms

Steps

Iters	Range		Point
8	5.216356433003023e+17	1.3896206539962956e+20	1.0056610449059809e+20
5	-8.662603811930578e+142	-2.4793126303145234e+142	-3.887249535662771e+142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	62
1	58	62
2	58	62

end0.0ms

sample2.1s

Algorithm

intervals

Results

491.0ms	9863×	body	80	nan
266.0ms	5077×	body	80	valid
214.0ms	853×	body	1280	valid
203.0ms	1014×	body	640	valid
145.0ms	596×	body	1280	nan
112.0ms	570×	body	640	nan
105.0ms	701×	body	320	valid
56.0ms	393×	body	320	nan
35.0ms	355×	body	160	valid
18.0ms	189×	body	160	nan