Details

sample346.0ms

Algorithm

intervals

Results

19.0ms	44×	body	1280	valid
10.0ms	38×	body	640	valid
9.0ms	135×	body	80	valid
4.0ms	23×	body	320	valid
2.0ms	16×	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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

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

rewrite66.0ms

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:

23.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
38.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
45.0ms	(* (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

prune280.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
54×	`prod-diff`
50×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow1`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`fma-def` `fma-neg`
5×	`frac-times`
4×	`tan-quot` `expm1-log1p-u` `flip3--` `flip3-+` `flip--` `flip-+` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 163

Calls

4 calls:

9.0ms	(+ (sqrt 1.0) (tan x))
56.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
11.0ms	(- (sqrt 1.0) (tan x))
17.0ms	(* (tan x) (tan x))

series207.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (sqrt 1.0) (tan x))
100.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
40.0ms	(- (sqrt 1.0) (tan x))
33.0ms	(* (tan x) (tan x))

simplify67.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	550	2052
1	2400	1381
2	5001	1359

prune316.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

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:

35.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
37.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	406	1046
1	1794	921
2	5002	874

prune275.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
72×	`*-un-lft-identity` `prod-diff`
64×	`add-cube-cbrt`
60×	`exp-sum`
46×	`log-prod`
42×	`sqrt-prod`
23×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
13×	`associate-r`
12×	`exp-prod`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l` `log-pow`
6×	`fma-neg` `difference-of-squares`
4×	`tan-quot` `expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`swap-sqr` `associate-*l/` `distribute-lft-out--`
2×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `exp-diff` `associate-*r/` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 185

Calls

4 calls:

109.0ms	(* (+ (sqrt 1.0) (tan x)) (log (exp (- (sqrt 1.0) (tan x)))))
11.0ms	(- (sqrt 1.0) (tan x))
15.0ms	(* (tan x) (tan x))
27.0ms	(exp (- (sqrt 1.0) (tan x)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (+ (sqrt 1.0) (tan x)) (log (exp (- (sqrt 1.0) (tan x)))))
39.0ms	(- (sqrt 1.0) (tan x))
32.0ms	(* (tan x) (tan x))
69.0ms	(exp (- (sqrt 1.0) (tan x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	623	2688
1	2457	1688
2	5002	1180

prune326.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes195.0ms

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	18	18
1	18	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

655.0ms	1524×	body	1280	valid
347.0ms	1277×	body	640	valid
240.0ms	4255×	body	80	valid
118.0ms	611×	body	320	valid
42.0ms	333×	body	160	valid