Details

sample86.0ms

Algorithm

intervals

Results

36.0ms	108×	body	2560	valid
20.0ms	72×	body	1280	valid
8.0ms	270×	body	80	nan
7.0ms	40×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	12×	body	80	valid

simplify96.0ms

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	2878	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 5.0 (* v v)))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

3.0ms	(- 1.0 (* 5.0 (* v v)))
8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- 1.0 (* 5.0 (* v v)))
87.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	391	750
1	1491	682
2	5002	678

prune247.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.1b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
1.0ms	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
126.0ms	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
29.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	361	749
1	1295	678
2	5001	676

prune236.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.0b	(expm1 (log1p (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))
0.1b	(* 5.0 (* v v))
0.6b	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

431×	`add-sqr-sqrt`
385×	`times-frac`
300×	`prod-diff`
265×	`*-un-lft-identity`
197×	`add-cube-cbrt`
164×	`difference-of-squares`
82×	`associate-/r/`
42×	`flip3--` `flip--`
41×	`div-inv`
34×	`distribute-lft-out--`
33×	`unpow-prod-down` `unpow2` `sqr-pow`
30×	`fma-neg`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`acos-asin` `sub-neg` `expm1-log1p` `diff-log` `associate-r` `*-commutative` `frac-sub` `expm1-udef` `unswap-sqr`

Counts

4 → 390

Calls

4 calls:

40.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
1.0ms	(expm1 (log1p (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))
6.0ms	(* 5.0 (* v v))
7.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
142.0ms	(expm1 (log1p (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))
32.0ms	(* 5.0 (* v v))
5.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify176.0ms

Algorithm

egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1151	13802
1	3272	9532
2	5001	9525

prune914.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.0b	(expm1 (log1p (- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))))
0.1b	(* 5.0 (* v v))
0.7b	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

431×	`add-sqr-sqrt`
385×	`times-frac`
300×	`prod-diff`
265×	`*-un-lft-identity`
197×	`add-cube-cbrt`
164×	`difference-of-squares`
82×	`associate-/r/`
42×	`flip3--` `flip--`
41×	`div-inv`
34×	`distribute-lft-out--`
33×	`unpow-prod-down` `unpow2` `sqr-pow`
30×	`fma-neg`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `asin-acos` `expm1-log1p` `diff-log` `associate-r` `*-commutative` `frac-sub` `expm1-udef` `unswap-sqr`

Counts

4 → 390

Calls

4 calls:

34.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
1.0ms	(expm1 (log1p (- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))))
6.0ms	(* 5.0 (* v v))
7.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
276.0ms	(expm1 (log1p (- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))))
25.0ms	(* 5.0 (* v v))
5.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify176.0ms

Algorithm

egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1162	13854
1	3311	9578
2	5001	9571

prune962.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes70.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	2978×	body	2560	valid
549.0ms	2475×	body	1280	valid
217.0ms	8063×	body	80	nan
210.0ms	1259×	body	640	valid
78.0ms	647×	body	320	valid
35.0ms	408×	body	160	valid
11.0ms	233×	body	80	valid