Details

sample306.0ms

Algorithm

intervals

Results

24.0ms	48×	body	1280	valid
14.0ms	36×	body	640	valid
11.0ms	139×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	10×	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:

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

rewrite29.0ms

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))

series221.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- 1.0 (* (tan x) (tan x)))
97.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

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

prune305.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
1.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series72.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)
18.0ms	(pow (sin x) 2)
22.0ms	(pow (sin x) 2)

simplify62.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	146	308
1	487	260
2	1671	260
3	5001	256

prune262.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 184

Calls

4 calls:

2.0ms	(- 1.0 (* (tan x) (tan x)))
4.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
8.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series280.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
105.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
106.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
36.0ms	(* (tan x) (tan x))

simplify80.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	593	2482
1	2691	2268
2	5001	2158

prune410.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
6×	`tan-quot` `associate-r` `associate-l` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip--` `flip-+`

Counts

4 → 117

Calls

4 calls:

5.0ms	(* (tan x) (sin x))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
19.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))

series248.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (tan x) (sin x))
59.0ms	(/ (* (tan x) (sin x)) (cos x))
111.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(* (tan x) (tan x))

simplify60.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	455	1207
1	1904	1097
2	5001	1088

prune322.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	11
1	15	11

end0.0ms

sample1.9s

Algorithm

intervals

Results

799.0ms	1569×	body	1280	valid
407.0ms	1221×	body	640	valid
333.0ms	4324×	body	80	valid
133.0ms	566×	body	320	valid
60.0ms	320×	body	160	valid