Details

sample99.0ms

Algorithm

intervals

Results

22.0ms	313×	body	80	nan
13.0ms	27×	body	640	valid
13.0ms	180×	body	80	valid
8.0ms	24×	body	1280	valid
6.0ms	17×	body	1280	nan
4.0ms	16×	body	640	nan
3.0ms	13×	body	320	valid
2.0ms	9×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	6×	body	160	nan

simplify98.0ms

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

prune10.0ms

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: 41.9b

Counts

2 → 1

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)
12.2b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite54.0ms

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)
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:

430.0ms	(/ (* (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)
214.0ms	(- (* (/ (+ 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

prune352.0ms

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: 5.0b

Counts

103 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.3b	(/ (pow l 2) x)
9.2b	(/ (pow t 2) x)
26.6b	(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)))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
24.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
268.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (34.0ms)

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

prune450.0ms

Filtered

139 candidates to 96 candidates (69.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	135	9	144

Merged error: 1.9b

Counts

144 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
3.6b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.2b	(/ (pow t 2) x)
26.6b	(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:

4.0ms	(* (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)))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt 2.0) t)
70.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow t 2) x)
269.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

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

prune368.0ms

Filtered

112 candidates to 78 candidates (69.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	110	11	121

Merged error: 1.9b

Counts

121 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
3.6b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.2b	(/ (pow t 2) x)
26.6b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 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 (/ 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)))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (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)
272.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (36.0ms)

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

prune351.0ms

Filtered

114 candidates to 78 candidates (68.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	112	13	125

Merged error: 1.9b

Counts

125 → 13

regimes547.0ms

Accuracy

76.5% (5.7b remaining)

Error of 9.5b against oracle of 3.7b and baseline of 28.2b

bsearch363.0ms

Steps

Iters	Range		Point
8	1.432459265546787e+83	5.5169350175537886e+85	2.1993251903526813e+85
7	-1.9014569726683186e-283	-3.019842982184082e-285	-2.3649775096023287e-284
3	-9.137979276603949e-166	-7.229263141007501e-166	-8.54150548423006e-166
5	-4.492037802898764e+71	-2.076790252128248e+71	-4.4153659189983183e+71

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	95
1	58	95

end0.0ms

sample2.8s

Algorithm

intervals

Results

714.0ms	10042×	body	80	nan
368.0ms	5137×	body	80	valid
288.0ms	824×	body	1280	valid
286.0ms	1007×	body	640	valid
195.0ms	561×	body	1280	nan
174.0ms	640×	body	640	nan
142.0ms	684×	body	320	valid
73.0ms	357×	body	320	nan
50.0ms	348×	body	160	valid
25.0ms	170×	body	160	nan