Details

sample83.0ms

Algorithm

intervals

Results

36.0ms	106×	body	2560	valid
15.0ms	66×	body	1280	valid
8.0ms	263×	body	80	nan
7.0ms	42×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	7×	body	80	valid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-sqr-sqrt`
3×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `associate-r` `*-commutative` `unswap-sqr`

Counts

2 → 31

Calls

2 calls:

16.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series26.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify111.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	124	206
1	355	176
2	960	176
3	3275	176
4	5001	176

prune273.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 3 expressions with local error:

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)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
45×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
13×	`fma-neg`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`div-inv`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`asin-acos` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `flip--` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

3 → 101

Calls

3 calls:

25.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
16.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series54.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
22.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify195.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (174.0ms)

Iter	Nodes	Cost
0	357	2531
1	1002	1460
2	4835	1437
3	5001	1428

prune181.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cube-cbrt`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `times-frac` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `cbrt-div` `flip3--` `unpow3` `flip--` `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 → 95

Calls

4 calls:

16.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
21.0ms	(cbrt (pow (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))
25.0ms	(pow (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)

series153.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
31.0ms	(cbrt (pow (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))
96.0ms	(pow (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)

simplify46.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	339	1327
1	1205	1245
2	5001	1239

prune210.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cube-cbrt`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `times-frac` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `cbrt-div` `flip3--` `unpow3` `flip--` `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 → 95

Calls

4 calls:

16.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
22.0ms	(cbrt (pow (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))
23.0ms	(pow (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)

series151.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
27.0ms	(cbrt (pow (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))
96.0ms	(pow (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	339	1327
1	1205	1245
2	5001	1239

prune258.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes78.0ms

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	19	13
1	19	13

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	2976×	body	2560	valid
575.0ms	2526×	body	1280	valid
243.0ms	8422×	body	80	nan
204.0ms	1241×	body	640	valid
77.0ms	647×	body	320	valid
34.0ms	406×	body	160	valid
10.0ms	204×	body	80	valid