Details

sample110.0ms

Algorithm

intervals

Results

23.0ms	336×	body	80	nan
17.0ms	16×	body	640	nan
12.0ms	34×	body	1280	valid
11.0ms	157×	body	80	valid
8.0ms	31×	body	640	valid
5.0ms	13×	body	1280	nan
4.0ms	21×	body	320	valid
4.0ms	19×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	5×	body	160	nan

simplify99.0ms

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: 47.0b

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)
18.3b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.1b	(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:

26.0ms	(/ (* (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)))

series1.9s

Counts

4 → 12

Calls

4 calls:

429.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
45.0ms	(* (sqrt 2.0) t)
216.0ms	(- (* (/ (+ 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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (52.0ms)

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

prune336.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	5	103

Merged error: 6.7b

Counts

103 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
9.0b	(/ (pow l 2) x)
10.9b	(/ (pow t 2) x)
30.2b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite16.0ms

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)))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(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)
24.0ms	(/ (pow t 2) x)
271.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (36.0ms)

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

prune444.0ms

Filtered

139 candidates to 96 candidates (69.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	133	11	144

Merged error: 3.8b

Counts

144 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
5.4b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
10.9b	(/ (pow t 2) x)
30.2b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

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:

4.0ms	(* (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)))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sqrt 2.0) t)
71.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
264.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	321	666
1	1291	592
2	5001	586

prune342.0ms

Filtered

112 candidates to 78 candidates (69.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 3.7b

Counts

123 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
5.4b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
10.9b	(/ (pow t 2) x)
30.2b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
17×	`pow1`
12×	`unpow-prod-down` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `pow-exp` `clear-num` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

14.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (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)))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (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)
264.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	371	843
1	1422	691
2	5002	641

prune324.0ms

Filtered

112 candidates to 75 candidates (67.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	110	13	123

Merged error: 3.7b

Counts

123 → 13

regimes450.0ms

Accuracy

76.8% (5.4b remaining)

Error of 9.4b against oracle of 3.9b and baseline of 27.3b

bsearch514.0ms

Steps

Iters	Range		Point
10	1.2595621310590059e+82	3.894835433597967e+93	2.258932197835794e+91
6	7.074655084320963e-174	3.1124934180468344e-173	3.030059721002767e-173
11	1.3206601388511477e-263	8.075482312126455e-244	2.85675210770605e-244
7	-5.2688144766041883e+36	-5.369753097786847e+34	-5.1993499904970025e+36

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	101
1	66	101
2	69	101
3	69	101

end0.0ms

sample2.6s

Algorithm

intervals

Results

671.0ms	10056×	body	80	nan
342.0ms	5067×	body	80	valid
292.0ms	882×	body	1280	valid
264.0ms	1034×	body	640	valid
183.0ms	570×	body	1280	nan
154.0ms	613×	body	640	nan
123.0ms	640×	body	320	valid
72.0ms	387×	body	320	nan
48.0ms	377×	body	160	valid
22.0ms	177×	body	160	nan