Details

sample80.0ms

Algorithm

intervals

Results

31.0ms	94×	body	2560	valid
19.0ms	73×	body	1280	valid
7.0ms	250×	body	80	nan
7.0ms	43×	body	640	valid
3.0ms	25×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	5×	body	80	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	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 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series111.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- 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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	336	587
1	1261	535
2	5002	531

prune166.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

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))
0.6b	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
32×	`associate-r`
28×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`sqrt-prod`
19×	`add-exp-log` `add-cbrt-cube`
16×	`pow1`
12×	`associate-l`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
7×	`pow-prod-down`
6×	`difference-of-squares`
4×	`sqrt-div` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--`
2×	`frac-times` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `acos-asin` `associate-*r/` `div-exp` `div-inv`

Counts

4 → 106

Calls

4 calls:

34.0ms	(* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))
7.0ms	(* 5.0 (* v v))
7.0ms	(* 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))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))
25.0ms	(* 5.0 (* v v))
29.0ms	(* 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))))

simplify55.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	441	1233
1	1917	1048
2	5001	1003

prune272.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (acos (* (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))
0.6b	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`exp-prod` `add-log-exp`
3×	`log-prod` `exp-sum`
2×	`associate-r` `*-commutative` `unswap-sqr`
1×	`acos-asin` `log-pow` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

2.0ms	(exp (log (acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))))
7.0ms	(* 5.0 (* v v))
7.0ms	(* 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))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (log (acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))))
29.0ms	(* 5.0 (* v v))
25.0ms	(* 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))))

simplify114.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	153	618
1	400	528
2	1033	492
3	3488	474
4	5003	474

prune179.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.6b	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))
0.6b	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
2×	`acos-asin` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

10.0ms	(* 5.0 (* v v))
7.0ms	(* 5.0 (* v v))
0.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))
1.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 5.0 (* v v))
24.0ms	(* 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))))
4.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify110.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	121	500
1	349	416
2	956	404
3	3263	404
4	5001	404

prune246.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes136.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	26
1	27	26

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	3012×	body	2560	valid
564.0ms	2513×	body	1280	valid
209.0ms	7845×	body	80	nan
197.0ms	1219×	body	640	valid
72.0ms	610×	body	320	valid
36.0ms	442×	body	160	valid
10.0ms	204×	body	80	valid