Details

sample79.0ms

Algorithm

intervals

Results

33.0ms	95×	body	2560	valid
19.0ms	87×	body	1280	valid
7.0ms	45×	body	640	valid
7.0ms	242×	body	80	nan
2.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	8×	body	80	valid

simplify97.0ms

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)))

rewrite16.0ms

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:

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)))

series115.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

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

prune162.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.6b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
29.0ms	(* 5.0 (* v v))
4.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	409	840
1	1459	784
2	5001	780

prune232.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize13.0ms

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	(- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
0.2b	(* 5.0 (* v v))
0.6b	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `asin-acos` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`
1×	`associate-r` `*-commutative` `frac-sub` `associate--r-` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

27.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
12.0ms	(- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
5.0ms	(* 5.0 (* v v))
7.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
32.0ms	(- (/ PI 2) (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))))
24.0ms	(* 5.0 (* v v))
5.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify144.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	325	837
1	1068	770
2	4840	764
3	5002	764

prune182.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.6b	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
1.0b	(cbrt (pow (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) 3))
1.0b	(pow (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) 3)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`add-log-exp`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `pow1/3` `associate-r` `pow-exp` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

6.0ms	(* 5.0 (* v v))
7.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
2.0ms	(cbrt (pow (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) 3))
12.0ms	(pow (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) 3)

series94.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 5.0 (* v v))
5.0ms	(asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))
5.0ms	(cbrt (pow (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) 3))
56.0ms	(pow (asin (- (/ 1.0 (- (pow v 2) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) 3)

simplify151.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	210	1011
1	739	926
2	3935	920
3	5002	920

prune178.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes31.0ms

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	20	14
1	20	14

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	2999×	body	2560	valid
559.0ms	2518×	body	1280	valid
222.0ms	7917×	body	80	nan
198.0ms	1219×	body	640	valid
75.0ms	632×	body	320	valid
36.0ms	415×	body	160	valid
10.0ms	217×	body	80	valid