Details

sample139.0ms

Algorithm

intervals

Results

44.0ms	333×	body	80	nan
18.0ms	168×	body	80	valid
15.0ms	32×	body	1280	valid
10.0ms	27×	body	640	valid
9.0ms	20×	body	1280	nan
8.0ms	23×	body	640	nan
7.0ms	24×	body	320	valid
2.0ms	7×	body	320	nan
1.0ms	5×	body	160	valid
1.0ms	5×	body	160	nan

simplify96.0ms

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: 44.2b

localize19.0ms

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)
14.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite75.0ms

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:

24.0ms	(/ (* (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)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
29.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

419.0ms	(/ (* (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)
211.0ms	(- (* (/ (+ 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)))

simplify67.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (53.0ms)

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

prune349.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.4b

localize21.0ms

Local error

Found 4 expressions with local error:

5.7b	(/ (pow l 2) x)
5.8b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
9.2b	(/ (pow t 2) x)
29.2b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

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:

4.0ms	(/ (pow l 2) x)
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow l 2) x)
68.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
266.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	377	811
1	1351	724
2	5001	715

prune472.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
5.8b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.2b	(/ (pow t 2) x)
29.2b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite13.0ms

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)
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt 2.0) t)
70.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
260.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	325	722
1	1269	642
2	5001	632

prune415.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
5.8b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.2b	(/ (pow t 2) x)
29.2b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite25.0ms

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:

16.0ms	(* (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))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
69.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
262.0ms	(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

114 → 114

Iterations

Useful iterations: 2 (37.0ms)

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

prune415.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.1b

regimes368.0ms

Accuracy

77.1% (5.5b remaining)

Error of 9.3b against oracle of 3.8b and baseline of 27.8b

bsearch314.0ms

Steps

Iters	Range		Point
11	2.3978422144747918e+88	1.8292938033907602e+110	2.0467080239710555e+93
10	-2.9582771485052574e+72	-2.98384958962079e+60	-2.9422530870118713e+66

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	56
1	49	56

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.0s	10037×	body	80	nan
547.0ms	5133×	body	80	valid
402.0ms	850×	body	1280	valid
379.0ms	1016×	body	640	valid
253.0ms	558×	body	1280	nan
224.0ms	620×	body	640	nan
176.0ms	628×	body	320	valid
91.0ms	328×	body	320	nan
71.0ms	373×	body	160	valid
34.0ms	182×	body	160	nan