Details

sample312.0ms

Algorithm

intervals

Results

25.0ms	55×	body	1280	valid
9.0ms	36×	body	640	valid
7.0ms	138×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	918
2	5001	882

prune294.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`associate-r`
20×	`pow1`
17×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `associate-r/` `prod-diff` `pow-prod-down` `-commutative` `flip--`
2×	`pow2` `pow-plus` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3-+` `diff-log` `1-exp` `un-div-inv` `flip-+` `div-inv`

Counts

4 → 126

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
18.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series190.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
91.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
31.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify58.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	406	1046
1	1794	920
2	5002	874

prune283.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
32×	`add-cube-cbrt`
23×	`times-frac`
21×	`prod-diff`
20×	`add-exp-log`
18×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow1`
8×	`associate-l`
6×	`prod-exp` `add-log-exp`
5×	`tan-quot` `div-inv`
4×	`expm1-log1p-u` `div-exp` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`cbrt-undiv` `frac-times` `flip3--` `fma-neg` `swap-sqr` `associate-/r*` `flip--`
2×	`associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `sub-neg` `rec-exp` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `1-exp` `clear-num` `pow-sqr` `un-div-inv` `pow-prod-up` `flip-+` `associate-/l/` `associate-/l*`

Counts

4 → 140

Calls

4 calls:

6.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
30.0ms	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series253.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
60.0ms	(/ (* (tan x) (sin x)) (cos x))
110.0ms	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))

simplify97.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	643	1948
1	3049	1532
2	5001	1510

prune388.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
44×	`add-cube-cbrt`
37×	`times-frac`
27×	`associate-r`
20×	`sqrt-prod`
18×	`prod-diff`
16×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--`
7×	`associate-l`
6×	`fma-neg` `associate-/l*` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`frac-times` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv` `associate-/l/`
1×	`pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `pow-sqr` `pow-prod-up` `distribute-lft-out`

Counts

4 → 167

Calls

4 calls:

17.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- (sqrt 1.0) (tan x))
43.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series355.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(- (sqrt 1.0) (tan x))
195.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))

simplify88.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	644	2081
1	3040	1700
2	5002	1673

prune382.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes178.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	8	9

end0.0ms

sample1.5s

Algorithm

intervals

Results

688.0ms	1544×	body	1280	valid
327.0ms	1205×	body	640	valid
247.0ms	4307×	body	80	valid
115.0ms	621×	body	320	valid
42.0ms	323×	body	160	valid