Details

sample409.0ms

Algorithm

intervals

Results

40.0ms	54×	body	640	valid
31.0ms	51×	body	1280	valid
12.0ms	163×	body	80	valid
4.0ms	18×	body	320	valid
2.0ms	15×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

22.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
20.0ms	(* x (/ 1.0 (tan B)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))
39.0ms	(/ 1.0 (tan B))
130.0ms	(* x (/ 1.0 (tan B)))

simplify50.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	696
1	1724	639
2	5002	635

prune362.0ms

Pruning

9 alts after pruning (9 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)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (* x 1.0) (tan B))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`fma-def`
18×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-neg-in`
8×	`distribute-lft-neg-in`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`tan-quot` `pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 91

Calls

3 calls:

56.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
14.0ms	(/ (* x 1.0) (tan B))

series265.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
119.0ms	(/ (* x 1.0) (tan B))

simplify37.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	350	492
1	1353	445
2	5002	440

prune284.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

107×	`times-frac`
68×	`*-un-lft-identity`
59×	`add-sqr-sqrt` `add-cube-cbrt`
56×	`fma-def`
32×	`add-exp-log`
29×	`distribute-rgt-neg-in`
26×	`distribute-lft-neg-in`
20×	`add-cbrt-cube`
16×	`div-inv`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/r/`
2×	`sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `pow-flip` `flip3-+` `neg-log` `frac-add` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 187

Calls

4 calls:

102.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
10.0ms	(/ (tan B) (* x 1.0))
18.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
55.0ms	(/ (tan B) (* x 1.0))
96.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	549	959
1	2347	844
2	5001	789

prune529.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (/ x (tan B)) 1.0 (- (/ 1.0 (sin B))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ x (tan B))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma (/ x (tan B)) 1.0 (- (/ 1.0 (sin B))))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ x (tan B))

series264.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(fma (/ x (tan B)) 1.0 (- (/ 1.0 (sin B))))
25.0ms	(/ 1.0 (sin B))
110.0ms	(/ x (tan B))

simplify56.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	250	412
1	720	379
2	2083	379
3	5001	375

prune234.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

988.0ms	1734×	body	1280	valid
493.0ms	1381×	body	640	valid
394.0ms	5007×	body	80	valid
174.0ms	703×	body	320	valid
65.0ms	361×	body	160	valid