Details

sample75.0ms

Algorithm

intervals

Results

14.0ms	300×	body	80	nan
8.0ms	164×	body	80	valid
7.0ms	28×	body	1280	valid
6.0ms	23×	body	1280	nan
5.0ms	28×	body	640	valid
4.0ms	29×	body	320	valid
2.0ms	13×	body	640	nan
1.0ms	10×	body	320	nan
1.0ms	7×	body	160	valid
0.0ms	3×	body	160	nan

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

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))))
0.4b	(* (sqrt 2.0) t)
15.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite146.0ms

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:

54.0ms	(/ (* (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)
33.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
46.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

438.0ms	(/ (* (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)
217.0ms	(- (* (/ (+ 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)))

simplify63.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (51.0ms)

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

prune354.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.7b

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))))
9.4b	(/ (pow l 2) x)
10.7b	(/ (pow t 2) x)
27.2b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite26.0ms

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:

68.0ms	(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)
25.0ms	(/ (pow t 2) x)
264.0ms	(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

prune466.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

localize22.0ms

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 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
10.7b	(/ (pow t 2) x)
27.2b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite22.0ms

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:

9.0ms	(* (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)))))

series386.0ms

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

simplify41.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (33.0ms)

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

prune401.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* t (sqrt 2.0))
4.4b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
10.7b	(/ (pow t 2) x)
27.2b	(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

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-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-l` `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:

9.0ms	(* t (sqrt 2.0))
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
11.0ms	(/ (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)))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* t (sqrt 2.0))
68.0ms	(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)
262.0ms	(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 (34.0ms)

Iter	Nodes	Cost
0	330	682
1	1259	615
2	5001	608

prune361.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

regimes488.0ms

Accuracy

76.1% (5.7b remaining)

Error of 9.6b against oracle of 3.9b and baseline of 27.9b

bsearch202.0ms

Steps

Iters	Range		Point
10	1.1309459419082891e+56	1.452376769013907e+67	9.991764826799716e+66
8	-1.470821775419402e+149	-4.770441291713145e+146	-4.834780474181416e+146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	55
1	52	55
2	52	55

end0.0ms

sample2.1s

Algorithm

intervals

Results

485.0ms	10148×	body	80	nan
255.0ms	5039×	body	80	valid
213.0ms	897×	body	1280	valid
177.0ms	963×	body	640	valid
124.0ms	550×	body	1280	nan
113.0ms	626×	body	640	nan
91.0ms	670×	body	320	valid
48.0ms	346×	body	320	nan
42.0ms	431×	body	160	valid
16.0ms	186×	body	160	nan