Details

sample112.0ms

Algorithm

intervals

Results

26.0ms	167×	body	80	valid
23.0ms	329×	body	80	nan
11.0ms	41×	body	640	valid
9.0ms	25×	body	1280	valid
5.0ms	15×	body	1280	nan
5.0ms	19×	body	640	nan
3.0ms	16×	body	320	nan
3.0ms	15×	body	320	valid
2.0ms	11×	body	160	nan
1.0ms	8×	body	160	valid

simplify100.0ms

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: 45.4b

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)
9.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite63.0ms

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:

17.0ms	(/ (* (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)
21.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

430.0ms	(/ (* (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)
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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (53.0ms)

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

prune329.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	4	103

Merged error: 5.2b

Counts

103 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.4b	(/ (pow l 2) x)
9.2b	(/ (pow t 2) x)
28.0b	(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)))))

series371.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(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)
263.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (35.0ms)

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

prune434.0ms

Filtered

139 candidates to 96 candidates (69.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 3.7b

Counts

143 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
4.0b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.2b	(/ (pow t 2) x)
28.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 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:

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

series386.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (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)
262.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	322	653
1	1220	592
2	5001	586

prune330.0ms

Filtered

112 candidates to 78 candidates (69.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Merged error: 3.7b

Counts

120 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.0b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.2b	(/ (pow t 2) x)
28.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite20.0ms

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

series401.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
70.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
264.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (37.0ms)

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

prune344.0ms

Filtered

114 candidates to 79 candidates (69.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	111	10	121

Merged error: 3.7b

Counts

121 → 10

regimes318.0ms

Accuracy

76% (5.7b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 27.2b

bsearch840.0ms

Steps

Iters	Range		Point
8	4.320864083551831e+86	2.815355964511566e+89	1.7591372474373838e+87
8	1.4269930238315257e-155	2.54528261745374e-151	1.4527325169532753e-155
9	2.266655187683933e-226	5.987044773231327e-217	1.9794607842594482e-217
8	1.981518881194765e-264	4.5878282246013355e-261	1.0063195590404383e-262
8	8.116575466757676e-304	2.645751865515408e-300	2.4757429114570086e-300
9	-8.818113417177725e+66	-2.444810577590085e+61	-5.780036183111328e+66

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	140
1	71	140

end0.0ms

sample2.7s

Algorithm

intervals

Results

678.0ms	9931×	body	80	nan
357.0ms	5125×	body	80	valid
284.0ms	850×	body	1280	valid
271.0ms	1038×	body	640	valid
190.0ms	574×	body	1280	nan
157.0ms	578×	body	640	nan
133.0ms	653×	body	320	valid
59.0ms	290×	body	320	nan
46.0ms	334×	body	160	valid
26.0ms	185×	body	160	nan