Details

sample110.0ms

Algorithm

intervals

Results

37.0ms	86×	body	2560	valid
30.0ms	86×	body	1280	valid
16.0ms	282×	body	80	nan
9.0ms	40×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	11×	body	80	valid

simplify95.0ms

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: 0.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 69

Calls

3 calls:

10.0ms	(/ (- 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)))

series116.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
7.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	349	623
1	1288	567
2	5001	565

prune182.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

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))))
0.1b	(* 5.0 (* v v))
0.6b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
49×	`times-frac`
39×	`prod-diff`
13×	`fma-neg`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
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` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 139

Calls

4 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
14.0ms	(- (/ 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)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
31.0ms	(- (/ 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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	576	2948
1	1941	1851
2	5003	1839

prune314.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4)))
0.0b	(- (/ PI 2) (asin (* (/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4))) (+ (* v v) 1.0))))
0.1b	(* 5.0 (* v v))
0.6b	(asin (* (/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4))) (+ (* v v) 1.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

6.0ms	(/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4)))
14.0ms	(- (/ PI 2) (asin (* (/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4))) (+ (* v v) 1.0))))
10.0ms	(* 5.0 (* v v))
1.0ms	(asin (* (/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4))) (+ (* v v) 1.0)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4)))
45.0ms	(- (/ PI 2) (asin (* (/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4))) (+ (* v v) 1.0))))
27.0ms	(* 5.0 (* v v))
9.0ms	(asin (* (/ (- 1.0 (* 5.0 (* v v))) (fma (- 1.0) 1.0 (pow v 4))) (+ (* v v) 1.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	545	3946
1	1817	2364
2	5002	2353

prune384.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b	(* 5.0 (* v v))
0.6b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(/ 1 (sqrt 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
0.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
3.0ms	(/ 1 (sqrt 2))

series120.0ms

Counts

4 → 10

Calls

4 calls:

87.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.0ms	(/ 1 (sqrt 2))

simplify50.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	447	849
1	1736	765
2	5001	738

prune324.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes86.0ms

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	20	13
1	20	13

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	2917×	body	2560	valid
779.0ms	2491×	body	1280	valid
452.0ms	8025×	body	80	nan
310.0ms	1273×	body	640	valid
114.0ms	640×	body	320	valid
59.0ms	452×	body	160	valid
21.0ms	227×	body	80	valid