Details

sample310.0ms

Algorithm

intervals

Results

18.0ms	39×	body	1280	valid
10.0ms	149×	body	80	valid
8.0ms	30×	body	640	valid
5.0ms	27×	body	320	valid
1.0ms	11×	body	160	valid

simplify15.0ms

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:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882

prune297.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

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)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
20.0ms	(* (- 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))

series189.0ms

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))

simplify59.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (48.0ms)

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

prune300.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.4b	(pow (* (tan x) (tan x)) 3)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

137×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
23×	`add-exp-log` `add-cbrt-cube`
21×	`pow-plus`
20×	`frac-times`
17×	`add-sqr-sqrt`
16×	`pow2`
14×	`associate-r/` `associate-l/`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`prod-exp` `cbrt-unprod`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative` `unswap-sqr`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 171

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
24.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
4.0ms	(pow (* (tan x) (tan x)) 3)

series179.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))
46.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
66.0ms	(pow (* (tan x) (tan x)) 3)

simplify57.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	388	622
1	1607	550
2	5001	539

prune370.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))

rewrite48.0ms

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:

5.0ms	(/ (* (tan x) (sin x)) (cos x))
6.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
28.0ms	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series257.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (* (tan x) (sin x)) (cos x))
50.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
110.0ms	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))

simplify99.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	643	1948
1	3050	1532
2	5002	1510

prune354.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes248.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

653.0ms	1498×	body	1280	valid
360.0ms	1318×	body	640	valid
255.0ms	4239×	body	80	valid
128.0ms	637×	body	320	valid
40.0ms	308×	body	160	valid