Details

sample129.0ms

Algorithm

intervals

Results

45.0ms	86×	body	2560	valid
34.0ms	82×	body	1280	valid
18.0ms	258×	body	80	nan
12.0ms	43×	body	640	valid
6.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	6×	body	80	valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- 1.0 (* 5.0 (* v v)))
0.2b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

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`
6×	`add-log-exp`
4×	`associate-/r*` `difference-of-squares`
3×	`flip3--` `associate-l` `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 → 75

Calls

4 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
2.0ms	(- 1.0 (* 5.0 (* v v)))
7.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
60.0ms	(- 1.0 (* 5.0 (* v v)))
25.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	355	664
1	1356	609
2	5001	605

prune388.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
0.0b	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.2b	(* 5.0 (* v v))
0.5b	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`times-frac`
4×	`associate-/r*` `difference-of-squares`
3×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
2×	`flip3--` `associate-/r/` `flip--`
1×	`acos-asin` `sub-neg` `frac-2neg` `diff-log` `associate-r` `clear-num` `-commutative` `frac-sub` `div-inv` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
80.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
7.0ms	(* 5.0 (* v v))
37.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
117.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
28.0ms	(* 5.0 (* v v))
5.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	409	726
1	1831	639
2	5002	637

prune203.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
0.0b	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.2b	(* 5.0 (* v v))
0.5b	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`times-frac`
4×	`associate-/r*` `difference-of-squares`
3×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
2×	`flip3--` `associate-/r/` `flip--`
1×	`sub-neg` `asin-acos` `frac-2neg` `diff-log` `associate-r` `clear-num` `-commutative` `frac-sub` `div-inv` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
82.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
7.0ms	(* 5.0 (* v v))
24.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (* 5.0 (* v v)) (- (* v v) 1.0))
123.0ms	(- (/ 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))))

simplify55.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	409	726
1	1831	639
2	5002	637

prune219.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
1.0b	(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
1.0b	(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
1.0b	(* (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))) (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

36.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
1.0ms	(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
7.0ms	(* (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))) (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
22.0ms	(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
25.0ms	(sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
6.0ms	(* (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))) (sqrt (acos (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

simplify124.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	129	1374
1	467	1206
2	2658	1144
3	5001	1101

prune184.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes25.0ms

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	17	12
1	17	12

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	2999×	body	2560	valid
956.0ms	2538×	body	1280	valid
564.0ms	8033×	body	80	nan
357.0ms	1224×	body	640	valid
135.0ms	617×	body	320	valid
66.0ms	414×	body	160	valid
22.0ms	208×	body	80	valid