Details

sample88.0ms

Algorithm

intervals

Results

31.0ms	86×	body	2560	valid
22.0ms	88×	body	1280	valid
12.0ms	244×	body	80	nan
7.0ms	40×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	18×	body	160	valid
0.0ms	5×	body	80	valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	43	7
2	84	7
3	155	7
4	262	7
5	454	7
6	2865	7
7	5002	7

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.4b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.3b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

351×	`add-sqr-sqrt`
126×	`difference-of-squares`
124×	`*-un-lft-identity`
110×	`times-frac`
85×	`unswap-sqr`
46×	`distribute-lft-out--`
32×	`add-cube-cbrt`
29×	`associate-l`
27×	`swap-sqr`
26×	`*-commutative`
18×	`associate-r`
11×	`associate-/l*`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
8×	`pow1`
3×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 199

Calls

3 calls:

30.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
9.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series125.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
27.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify93.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	592	2114
1	2057	2019
2	5001	1982

prune242.0ms

Filtered

208 candidates to 94 candidates (54.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	205	3	208
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	206	3	209

Merged error: 0.3b

Counts

209 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
0.2b	(* 5.0 (* v v))
0.3b	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

1375×	`add-sqr-sqrt`
788×	`times-frac`
565×	`*-un-lft-identity`
471×	`difference-of-squares`
298×	`unswap-sqr`
216×	`add-cube-cbrt`
174×	`distribute-lft-out--`
127×	`associate-/r*`
93×	`associate-l`
90×	`swap-sqr`
89×	`*-commutative`
34×	`associate-/r/`
19×	`add-exp-log`
18×	`associate-r`
16×	`associate-/l*`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`remove-double-div`
3×	`cbrt-undiv` `expm1-log1p-u` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-/l/`
1×	`acos-asin` `pow-flip` `inv-pow`

Counts

3 → 568

Calls

3 calls:

47.0ms	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
9.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

series123.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
27.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

simplify120.0ms

Algorithm

egg-herbie

Counts

577 → 577

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1298	7575
1	5001	6688

prune504.0ms

Filtered

577 candidates to 177 candidates (69.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	574	3	577
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	577	3	580

Merged error: 0.3b

Counts

580 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
0.0b	(expm1 (log1p (acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))))
0.2b	(* 5.0 (* v v))
0.3b	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

1376×	`add-sqr-sqrt`
788×	`times-frac`
566×	`*-un-lft-identity`
471×	`difference-of-squares`
298×	`unswap-sqr`
217×	`add-cube-cbrt`
174×	`distribute-lft-out--`
127×	`associate-/r*`
93×	`associate-l`
90×	`swap-sqr`
89×	`*-commutative`
34×	`associate-/r/`
20×	`add-exp-log`
18×	`associate-r`
16×	`associate-/l*`
14×	`add-cbrt-cube`
10×	`pow1`
7×	`div-exp`
5×	`flip3--` `flip--` `log1p-expm1-u` `div-inv`
4×	`expm1-log1p-u` `remove-double-div` `add-log-exp`
3×	`cbrt-undiv` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod`
2×	`rec-exp` `expm1-log1p` `frac-2neg` `1-exp` `associate-/l/`
1×	`acos-asin` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 580

Calls

4 calls:

48.0ms	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
1.0ms	(expm1 (log1p (acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))))
9.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
152.0ms	(expm1 (log1p (acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))))
26.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

simplify127.0ms

Algorithm

egg-herbie

Counts

592 → 592

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1310	7714
1	5001	6810

prune637.0ms

Filtered

592 candidates to 187 candidates (68.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	591	1	592
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	592	3	595

Merged error: 0.3b

Counts

595 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))
0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.3b	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

510×	`add-sqr-sqrt`
187×	`*-un-lft-identity`
182×	`associate-r`
169×	`difference-of-squares`
159×	`sqrt-prod`
144×	`times-frac`
121×	`unswap-sqr`
66×	`sqrt-div`
62×	`add-cube-cbrt` `distribute-lft-out--`
58×	`frac-times`
57×	`associate-l`
43×	`associate-/l*`
39×	`swap-sqr`
38×	`*-commutative`
34×	`flip3--` `flip--`
30×	`associate-/r*`
29×	`associate-*r/`
19×	`add-exp-log` `add-cbrt-cube`
16×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/l/`
4×	`expm1-log1p-u` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg`
2×	`associate-*l/` `associate-/r/` `un-div-inv`
1×	`cbrt-undiv` `acos-asin` `div-exp` `div-inv`

Counts

4 → 360

Calls

4 calls:

90.0ms	(* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))
9.0ms	(* 5.0 (* v v))
9.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))
36.0ms	(* 5.0 (* v v))
27.0ms	(* 5.0 (* v v))
4.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify148.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	963	4714
1	3910	4397
2	5001	4356

prune614.0ms

Filtered

372 candidates to 179 candidates (51.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	372	0	372
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	372	3	375

Merged error: 0.3b

Counts

375 → 3

regimes35.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	10
1	16	10

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	2919×	body	2560	valid
621.0ms	2465×	body	1280	valid
233.0ms	7957×	body	80	nan
231.0ms	1324×	body	640	valid
77.0ms	614×	body	320	valid
41.0ms	456×	body	160	valid
12.0ms	222×	body	80	valid