Details

sample349.0ms

Algorithm

intervals

Results

21.0ms	48×	body	1280	valid
12.0ms	45×	body	640	valid
8.0ms	135×	body	80	valid
3.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 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))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`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×	`associate-/l*`
3×	`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 → 105

Calls

4 calls:

22.0ms	(/ (- 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))

series192.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
30.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune243.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `log-pow`
18×	`exp-prod`
12×	`times-frac`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`difference-of-squares`
3×	`log-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `flip--` `flip-+` `div-inv`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
26.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- 1.0 (* (tan x) (tan x)))
29.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
86.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify140.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (132.0ms)

Iter	Nodes	Cost
0	289	756
1	888	687
2	3990	673
3	5001	667

prune255.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
21×	`-un-lft-identity` `associate-l*`
20×	`pow1` `add-cube-cbrt`
17×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`associate-r`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`frac-times` `associate-*r/` `cbrt-unprod`
3×	`sub-neg` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`
2×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`cbrt-undiv` `rec-exp` `flip3-+` `diff-log` `1-exp` `flip-+` `div-inv`

Counts

4 → 115

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(* (/ 1 (+ 1.0 (* (tan x) (tan x)))) (- 1.0 (* (tan x) (tan x))))
17.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))

series177.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- 1.0 (* (tan x) (tan x)))
86.0ms	(* (/ 1 (+ 1.0 (* (tan x) (tan x)))) (- 1.0 (* (tan x) (tan x))))
29.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

simplify56.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	382	1004
1	1641	889
2	5001	861

prune250.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

15.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
52.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series239.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
144.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify35.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	266	869
1	914	800
2	5002	784

prune203.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes131.0ms

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	9	14
1	9	14

end0.0ms

sample1.6s

Algorithm

intervals

Results

720.0ms	1596×	body	1280	valid
346.0ms	1259×	body	640	valid
234.0ms	4230×	body	80	valid
114.0ms	615×	body	320	valid
38.0ms	300×	body	160	valid