Details

sample304.0ms

Algorithm

intervals

Results

18.0ms	36×	body	1280	valid
14.0ms	44×	body	640	valid
13.0ms	150×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	8×	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))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
38.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (34.0ms)

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

prune285.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u`
3×	`fma-neg` `prod-diff`
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×	`sub-neg` `log1p-udef` `flip3--` `diff-log` `log1p-expm1` `flip--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
0.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
219.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

simplify135.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	246	612
1	827	546
2	3956	530
3	5001	525

prune252.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(log (exp (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)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
18×	`add-sqr-sqrt`
14×	`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×	`log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
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` `log1p-expm1` `rem-log-exp`

Counts

4 → 88

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
1.0ms	(log (exp (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)))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
219.0ms	(log (exp (log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))))
224.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	197	768
1	615	669
2	2646	645
3	5001	639

prune265.0ms

Pruning

9 alts after pruning (9 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))) (- (sqrt 1.0) (tan x))))
0.2b	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
0.2b	(- (sqrt 1.0) (tan x))
0.3b	(* (tan x) (tan x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
198×	`*-un-lft-identity`
190×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
40×	`difference-of-squares`
32×	`sqrt-prod`
30×	`associate-/r*`
25×	`distribute-lft-out`
20×	`distribute-lft-out--`
18×	`prod-diff`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`flip3--` `flip--` `div-inv` `associate-/l*`
6×	`fma-neg` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l/`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 259

Calls

4 calls:

27.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
14.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
6.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series378.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
115.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
36.0ms	(- (sqrt 1.0) (tan x))
33.0ms	(* (tan x) (tan x))

simplify122.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	818	4584
1	3992	3983
2	5001	3963

prune543.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes176.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	8
1	14	8
2	14	8

end0.0ms

sample1.8s

Algorithm

intervals

Results

747.0ms	1528×	body	1280	valid
409.0ms	1244×	body	640	valid
336.0ms	4289×	body	80	valid
143.0ms	610×	body	320	valid
56.0ms	329×	body	160	valid