Details

sample383.0ms

Algorithm

intervals

Results

28.0ms	58×	body	1280	valid
14.0ms	50×	body	640	valid
7.0ms	129×	body	80	valid
2.0ms	9×	body	320	valid
1.0ms	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: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite68.0ms

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:

24.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

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

prune302.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

36.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
13.0ms	(* (tan x) (sin x))
11.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
17.0ms	(* (tan x) (tan x))

series246.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
43.0ms	(* (tan x) (sin x))
55.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
33.0ms	(* (tan x) (tan x))

simplify84.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	560	1909
1	2268	1535
2	5001	1475

prune375.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 159

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
17.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma (tan x) (tan x) 1.0)
108.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
37.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(* (tan x) (tan x))

simplify70.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	570	2046
1	2617	1859
2	5002	1752

prune340.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
70×	`add-cube-cbrt`
57×	`times-frac`
54×	`prod-diff`
35×	`sqrt-prod`
33×	`associate-/r/`
27×	`add-exp-log`
20×	`distribute-rgt-in` `frac-times` `distribute-lft-in`
16×	`flip3--` `flip3-+` `flip--` `flip-+`
15×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`associate-r/` `associate-l/`
8×	`add-log-exp`
7×	`pow1`
6×	`fma-def` `fma-neg` `associate-r`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `rec-exp` `1-exp` `associate-/l*`
2×	`cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `pow-flip` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 223

Calls

4 calls:

41.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))))
11.0ms	(- (sqrt 1.0) (tan x))
56.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
12.0ms	(+ (sqrt 1.0) (tan x))

series378.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))))
37.0ms	(- (sqrt 1.0) (tan x))
103.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
35.0ms	(+ (sqrt 1.0) (tan x))

simplify107.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	877	3831
1	4413	2824
2	5001	2813

prune464.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes163.0ms

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	11	9
1	11	9

end0.0ms

sample1.6s

Algorithm

intervals

Results

696.0ms	1500×	body	1280	valid
349.0ms	1231×	body	640	valid
246.0ms	4304×	body	80	valid
125.0ms	636×	body	320	valid
48.0ms	329×	body	160	valid