Details

sample85.0ms

Algorithm

intervals

Results

39.0ms	70×	body	1280	valid
15.0ms	159×	body	80	valid
14.0ms	40×	body	640	valid
5.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify10.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (tan B))
0.2b	(/ 1.0 (sin B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite24.0ms

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:

7.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (tan B))
3.0ms	(/ 1.0 (sin B))
7.0ms	(* x (/ 1.0 (tan B)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
33.0ms	(/ 1.0 (tan B))
28.0ms	(/ 1.0 (sin B))
125.0ms	(* x (/ 1.0 (tan B)))

simplify54.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (46.0ms)

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

prune296.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

14.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
5.0ms	(/ (* x 1.0) (tan B))

series236.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
106.0ms	(/ (* x 1.0) (tan B))

simplify40.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	336	465
1	1303	419
2	5001	414

prune186.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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))

rewrite22.0ms

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:

7.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
4.0ms	(* x (cos B))
4.0ms	(/ 1.0 (sin B))
5.0ms	(/ (* x (cos B)) (sin B))

series248.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
37.0ms	(* x (cos B))
18.0ms	(/ 1.0 (sin B))
93.0ms	(/ (* x (cos B)) (sin B))

simplify47.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (40.0ms)

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

prune226.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 107

Calls

4 calls:

3.0ms	(/ 1.0 (sin B))
3.0ms	(/ 1.0 (sin B))
9.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
7.0ms	(* x (/ 1.0 (sin B)))

series188.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
20.0ms	(/ 1.0 (sin B))
98.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
52.0ms	(* x (/ 1.0 (sin B)))

simplify52.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	315	645
1	1562	560
2	5001	560

prune272.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes76.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	9
1	22	9
2	28	9
3	28	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

956.0ms	1663×	body	1280	valid
518.0ms	1424×	body	640	valid
393.0ms	4953×	body	80	valid
167.0ms	707×	body	320	valid
66.0ms	395×	body	160	valid