Details

sample337.0ms

Algorithm

intervals

Results

34.0ms	59×	body	1280	valid
18.0ms	53×	body	640	valid
13.0ms	138×	body	80	valid
6.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

21.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
11.0ms	(* x (/ 1.0 (tan B)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
123.0ms	(* x (/ 1.0 (tan B)))

simplify52.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	419	664
1	1645	609
2	5001	604

prune321.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
0.1b	(* x (cos B))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

9.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
3.0ms	(* x (cos B))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x (cos B)) (sin B))

series255.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
38.0ms	(* x (cos B))
19.0ms	(/ 1.0 (sin B))
96.0ms	(/ (* x (cos B)) (sin B))

simplify47.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	359	603
1	1463	536
2	5002	530

prune244.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 (/ (* x (cos B)) (sin B))) (/ 1.0 (sin B)))
0.1b	(* x (cos B))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

9.0ms	(- (* 1.0 (/ (* x (cos B)) (sin B))) (/ 1.0 (sin B)))
3.0ms	(* x (cos B))
2.0ms	(/ 1.0 (sin B))
6.0ms	(/ (* x (cos B)) (sin B))

series257.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (* 1.0 (/ (* x (cos B)) (sin B))) (/ 1.0 (sin B)))
35.0ms	(* x (cos B))
18.0ms	(/ 1.0 (sin B))
95.0ms	(/ (* x (cos B)) (sin B))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	333	569
1	1339	508
2	5001	505

prune240.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos B)) (cbrt (cos B)))
0.4b	(cbrt (cos B))
0.4b	(cbrt (cos B))
0.4b	(cbrt (cos B))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
1.0ms	(cbrt (cos B))
1.0ms	(cbrt (cos B))
1.0ms	(cbrt (cos B))

series449.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
97.0ms	(cbrt (cos B))
96.0ms	(cbrt (cos B))
99.0ms	(cbrt (cos B))

simplify108.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	122	441
1	481	389
2	3180	357
3	5001	351

prune244.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes66.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1737×	body	1280	valid
515.0ms	1420×	body	640	valid
397.0ms	4887×	body	80	valid
182.0ms	704×	body	320	valid
62.0ms	361×	body	160	valid