Details

sample80.0ms

Algorithm

intervals

Results

22.0ms	317×	body	80	nan
8.0ms	165×	body	80	valid
8.0ms	32×	body	1280	valid
6.0ms	29×	body	640	valid
4.0ms	24×	body	640	nan
3.0ms	13×	body	1280	nan
3.0ms	18×	body	320	valid
1.0ms	10×	body	320	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	160	nan

simplify94.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.1b

Counts

2 → 1

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))))
0.4b	(* (sqrt 2.0) t)
11.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite60.0ms

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)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

417.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
38.0ms	(* (sqrt 2.0) t)
215.0ms	(- (* (/ (+ 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 (50.0ms)

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

prune354.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Merged error: 7.1b

Counts

103 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

2.4b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.3b	(/ (pow l 2) x)
6.7b	(/ (pow t 2) x)
24.1b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite20.0ms

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)
5.0ms	(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:

66.0ms	(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)
18.0ms	(/ (pow t 2) x)
263.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (32.0ms)

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

prune482.0ms

Filtered

139 candidates to 96 candidates (69.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 4.7b

Counts

145 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
2.4b	(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
6.7b	(/ (pow t 2) x)
24.1b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite18.0ms

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:

8.0ms	(* (sqrt 2.0) t)
1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sqrt 2.0) t)
61.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
17.0ms	(/ (pow t 2) x)
141.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	356	727
1	1467	654
2	5001	649

prune417.0ms

Filtered

112 candidates to 79 candidates (70.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	113	11	124

Merged error: 4.7b

Counts

124 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
2.4b	(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
6.7b	(/ (pow t 2) x)
24.1b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite19.0ms

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:

9.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series265.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
55.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
146.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	396	807
1	1531	702
2	5001	693

prune417.0ms

Filtered

114 candidates to 80 candidates (70.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	113	12	125

Merged error: 4.7b

Counts

125 → 12

regimes529.0ms

Accuracy

77.6% (5.3b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 27.9b

bsearch317.0ms

Steps

Iters	Range		Point
8	1.2904779615766892e+141	7.028027817791006e+144	1.685885701146353e+141
5	-1.4953326436467958e-263	-4.242125608336209e-264	-1.4728195123242452e-263
5	-6.754176268358103e-154	-3.315251958224177e-154	-3.3628327780434735e-154
8	-8.015653944520392e+129	-3.707972559077159e+126	-5.0552001959163884e+126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	97
1	62	97

end0.0ms

sample2.0s

Algorithm

intervals

Results

497.0ms	10105×	body	80	nan
249.0ms	5029×	body	80	valid
220.0ms	883×	body	1280	valid
208.0ms	1064×	body	640	valid
134.0ms	556×	body	1280	nan
110.0ms	590×	body	640	nan
97.0ms	668×	body	320	valid
50.0ms	341×	body	320	nan
34.0ms	356×	body	160	valid
19.0ms	186×	body	160	nan