Details

sample304.0ms

Algorithm

intervals

Results

17.0ms	39×	body	1280	valid
10.0ms	149×	body	80	valid
8.0ms	30×	body	640	valid
5.0ms	27×	body	320	valid
1.0ms	11×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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

rewrite26.0ms

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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
55.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

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

prune264.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.4b	(pow (* (tan x) (tan x)) 3)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`tan-quot`
13×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-pow`
4×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative` `unswap-sqr`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))
4.0ms	(pow (* (tan x) (tan x)) 3)

series162.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))
63.0ms	(pow (* (tan x) (tan x)) 3)

simplify42.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	211	452
1	971	401
2	5001	384

prune325.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))
30.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))
152.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (29.0ms)

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

prune254.0ms

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 (sin x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
0.3b	(- (* 1.0 (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1.0))) (/ (pow (sin x) 2) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1.0) (pow (cos x) 2))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
2×	`frac-sub`
1×	`sub-neg` `flip3--` `diff-log` `associate-*r/` `un-div-inv` `flip--`

Counts

4 → 68

Calls

4 calls:

1.0ms	(pow (sin x) 2)
1.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)
44.0ms	(- (* 1.0 (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1.0))) (/ (pow (sin x) 2) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1.0) (pow (cos x) 2))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
21.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)
195.0ms	(- (* 1.0 (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1.0))) (/ (pow (sin x) 2) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1.0) (pow (cos x) 2))))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	216	743
1	879	666
2	5001	641

prune207.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes280.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	21
1	20	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

667.0ms	1498×	body	1280	valid
358.0ms	1318×	body	640	valid
238.0ms	4239×	body	80	valid
125.0ms	637×	body	320	valid
45.0ms	308×	body	160	valid