Details

sample105.0ms

Algorithm

intervals

Results

22.0ms	310×	body	80	nan
14.0ms	23×	body	1280	nan
11.0ms	159×	body	80	valid
10.0ms	36×	body	640	valid
10.0ms	28×	body	1280	valid
5.0ms	18×	body	640	nan
4.0ms	22×	body	320	valid
3.0ms	14×	body	320	nan
2.0ms	13×	body	160	nan
2.0ms	11×	body	160	valid

simplify97.0ms

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: 45.2b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (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)
15.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite62.0ms

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:

25.0ms	(/ (* (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))
15.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

420.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
44.0ms	(* (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)))

simplify70.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (52.0ms)

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

prune331.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	7	103

Merged error: 6.5b

Counts

103 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

2.6b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.2b	(/ (pow l 2) x)
10.3b	(/ (pow t 2) x)
27.9b	(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)))))

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))))
18.0ms	(/ (pow l 2) x)
23.0ms	(/ (pow t 2) x)
267.0ms	(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 (34.0ms)

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

prune445.0ms

Filtered

139 candidates to 96 candidates (69.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	133	13	146

Merged error: 3.5b

Counts

146 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
2.6b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
10.3b	(/ (pow t 2) x)
27.9b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite16.0ms

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 (* l (/ 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 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sqrt 2.0) t)
69.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
261.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	321	653
1	1261	592
2	5001	586

prune343.0ms

Filtered

112 candidates to 78 candidates (69.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	113	12	125

Merged error: 3.5b

Counts

125 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t)) (sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))))
2.6b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
10.3b	(/ (pow t 2) x)
27.9b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`times-frac`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log`
15×	`add-cbrt-cube`
12×	`unpow-prod-down`
9×	`associate-/r` `sqrt-prod` `associate-/l`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `fma-udef`

Counts

4 → 107

Calls

4 calls:

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

series507.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t)) (sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))))
69.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
263.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	427	1198
1	1986	1032
2	5001	1016

prune348.0ms

Filtered

119 candidates to 81 candidates (68.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	118	13	131

Merged error: 3.5b

Counts

131 → 13

regimes495.0ms

Accuracy

73.5% (6.3b remaining)

Error of 9.8b against oracle of 3.5b and baseline of 27.2b

bsearch845.0ms

Steps

Iters	Range		Point
10	4.303922473367365e+108	1.931316243244326e+118	8.28827763547494e+114
7	5.834548822037511e-190	5.310846843265014e-188	3.179593151054512e-188
8	2.0531948601770492e-296	1.9147608801785507e-293	1.8906625567539152e-293
9	1.602615327513597e-304	1.997368604160002e-299	1.617668931297377e-304
10	-1.3111885523472323e-180	-7.354709209583203e-196	-1.492381997315763e-189
9	-4.927324273936486e+121	-1.6988174615908472e+112	-1.5746361320052905e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	120
1	66	120
2	69	120
3	69	120

end0.0ms

sample2.7s

Algorithm

intervals

Results

693.0ms	9963×	body	80	nan
363.0ms	5153×	body	80	valid
291.0ms	860×	body	1280	valid
252.0ms	937×	body	640	valid
197.0ms	591×	body	1280	nan
158.0ms	592×	body	640	nan
144.0ms	705×	body	320	valid
70.0ms	360×	body	320	nan
50.0ms	345×	body	160	valid
25.0ms	188×	body	160	nan