Details

sample313.0ms

Algorithm

intervals

Results

21.0ms	49×	body	1280	valid
13.0ms	39×	body	640	valid
7.0ms	131×	body	80	valid
5.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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))

rewrite70.0ms

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:

6.0ms	(- 1.0 (* (tan x) (tan x)))
19.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
24.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series196.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- 1.0 (* (tan x) (tan x)))
89.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(* (tan x) (tan x))
41.0ms	(* (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

prune292.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)

rewrite15.0ms

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:

3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)

series69.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (cos x) 2)
15.0ms	(pow (cos x) 2)
17.0ms	(pow (sin x) 2)
18.0ms	(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

prune251.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
0.3b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 82

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
0.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
17.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))

series554.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
218.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
29.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))

simplify98.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	204	664
1	683	574
2	2965	552
3	5001	546

prune229.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
186×	`*-un-lft-identity`
174×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
38×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
22×	`sqrt-prod`
19×	`distribute-lft-out--`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `fma-def` `flip--` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l/`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 238

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
49.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
37.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
15.0ms	(* (tan x) (tan x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (sqrt 1.0) (tan x))
176.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
101.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
29.0ms	(* (tan x) (tan x))

simplify117.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	758	4210
1	3856	3784
2	5001	3760

prune538.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes231.0ms

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	12	13
1	12	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

675.0ms	1497×	body	1280	valid
363.0ms	1283×	body	640	valid
255.0ms	4285×	body	80	valid
116.0ms	608×	body	320	valid
43.0ms	327×	body	160	valid