Details

sample157.0ms

Algorithm

intervals

Results

49.0ms	331×	body	80	nan
23.0ms	167×	body	80	valid
19.0ms	36×	body	1280	valid
11.0ms	22×	body	1280	nan
11.0ms	25×	body	640	valid
7.0ms	15×	body	640	nan
6.0ms	19×	body	320	valid
5.0ms	15×	body	320	nan
2.0ms	9×	body	160	valid
1.0ms	5×	body	160	nan

simplify93.0ms

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: 40.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
0.4b	(* (sqrt 2.0) t)
12.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`associate-l`
21×	`times-frac`
19×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`sqrt-prod`
6×	`associate-r` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `sqrt-div` `associate-r/` `pow-prod-down` `associate--l+` `associate-/r/` `-commutative` `flip-+`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `associate-*l/` `div-inv`

Counts

4 → 112

Calls

4 calls:

36.0ms	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
5.0ms	(* (sqrt 2.0) t)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
24.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.5s

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
43.0ms	(* (sqrt 2.0) t)
207.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify99.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	738	1242
1	4095	1150
2	5001	1147

prune442.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.3b	(/ (pow l 2) x)
7.8b	(/ (pow t 2) x)
24.0b	(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:

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

series365.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(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)
262.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (34.0ms)

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

prune462.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
4.4b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
7.8b	(/ (pow t 2) x)
24.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ 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 (/ l (/ 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 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sqrt 2.0) t)
66.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
255.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	322	666
1	1250	592
2	5001	586

prune371.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.4b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
7.8b	(/ (pow t 2) x)
24.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite27.0ms

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:

19.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ 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 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
68.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
259.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	359	733
1	1286	640
2	5001	630

prune372.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

regimes518.0ms

Accuracy

77.7% (5.3b remaining)

Error of 8.9b against oracle of 3.6b and baseline of 27.5b

bsearch285.0ms

Steps

Iters	Range		Point
9	1.9180625303009828e+101	4.5691173792327456e+110	3.415486298780927e+106
8	-8.447359763721527e+131	-1.808868357531764e+127	-7.02224939412324e+130

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	65
1	60	65

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	10201×	body	80	nan
705.0ms	5099×	body	80	valid
445.0ms	833×	body	1280	valid
439.0ms	1030×	body	640	valid
301.0ms	584×	body	1280	nan
240.0ms	574×	body	640	nan
217.0ms	660×	body	320	valid
113.0ms	339×	body	320	nan
88.0ms	378×	body	160	valid
42.0ms	183×	body	160	nan