Details

sample302.0ms

Algorithm

intervals

Results

22.0ms	49×	body	1280	valid
14.0ms	44×	body	640	valid
8.0ms	142×	body	80	valid
2.0ms	11×	body	320	valid
1.0ms	10×	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:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (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:

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))
7.0ms	(* (tan x) (tan x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
54.0ms	(* (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

prune248.0ms

Pruning

14 alts after pruning (14 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))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sqrt-prod` `*-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 → 89

Calls

4 calls:

4.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(- (sqrt 1.0) (tan x))
30.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (sqrt 1.0) (tan x))
40.0ms	(- (sqrt 1.0) (tan x))
105.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
32.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	328	693
1	1582	618
2	5001	607

prune253.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
18×	`exp-prod`
16×	`add-cube-cbrt`
15×	`pow1` `log-prod`
14×	`log-pow`
13×	`associate-r`
8×	`add-exp-log` `exp-sum` `add-cbrt-cube`
7×	`associate-l` `add-log-exp`
6×	`difference-of-squares`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`tan-quot` `sub-neg`
3×	`swap-sqr` `associate-*l/` `sqrt-prod` `distribute-lft-out--`
2×	`exp-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`pow2` `frac-times` `log-div` `flip3-+` `pow-plus` `diff-log` `associate-*r/` `rem-log-exp` `pow-sqr` `pow-prod-up` `flip-+` `distribute-lft-out`

Counts

4 → 105

Calls

4 calls:

59.0ms	(* (+ (sqrt 1.0) (tan x)) (log (exp (- (sqrt 1.0) (tan x)))))
13.0ms	(log (exp (- (sqrt 1.0) (tan x))))
5.0ms	(* (tan x) (tan x))
12.0ms	(exp (- (sqrt 1.0) (tan x)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (+ (sqrt 1.0) (tan x)) (log (exp (- (sqrt 1.0) (tan x)))))
37.0ms	(log (exp (- (sqrt 1.0) (tan x))))
35.0ms	(* (tan x) (tan x))
71.0ms	(exp (- (sqrt 1.0) (tan x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	357	824
1	1499	703
2	5002	676

prune298.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 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))))))

rewrite30.0ms

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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
15.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
35.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
94.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify138.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (130.0ms)

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

prune240.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes172.0ms

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	13	10
1	13	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

692.0ms	1522×	body	1280	valid
387.0ms	1334×	body	640	valid
244.0ms	4210×	body	80	valid
124.0ms	646×	body	320	valid
38.0ms	288×	body	160	valid