Details

sample315.0ms

Algorithm

intervals

Results

25.0ms	55×	body	1280	valid
9.0ms	36×	body	640	valid
7.0ms	138×	body	80	valid
4.0ms	23×	body	320	valid
0.0ms	4×	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))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite27.0ms

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))

series213.0ms

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))

simplify46.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune236.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (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))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

16.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- (sqrt 1.0) (tan x))
31.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series363.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(- (sqrt 1.0) (tan x))
105.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
31.0ms	(* (tan x) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	520	1144
1	2857	962
2	5002	947

prune292.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (tan x) (sin x))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(/ (* (tan x) (sin x)) (cos x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`pow1`
7×	`associate-l`
6×	`add-log-exp`
4×	`frac-times` `flip3--` `associate-*l/` `flip--` `difference-of-squares`
3×	`sub-neg` `flip3-+` `times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `flip-+`
2×	`tan-quot` `cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `associate-r/` `div-exp` `pow-prod-down` `sqrt-prod` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l*`

Counts

4 → 90

Calls

4 calls:

5.0ms	(* (tan x) (sin x))
5.0ms	(- (sqrt 1.0) (tan x))
29.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(/ (* (tan x) (sin x)) (cos x))

series249.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (tan x) (sin x))
40.0ms	(- (sqrt 1.0) (tan x))
105.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
60.0ms	(/ (* (tan x) (sin x)) (cos x))

simplify57.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	408	777
1	2091	688
2	5001	681

prune316.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (tan x) (sin x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.3b	(* (tan x) (tan x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt`
6×	`tan-quot` `associate-r` `associate-l` `add-log-exp`
3×	`times-frac` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 83

Calls

4 calls:

5.0ms	(* (tan x) (sin x))
4.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (tan x))

series188.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (tan x) (sin x))
53.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
57.0ms	(/ (* (tan x) (sin x)) (cos x))
36.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	291	567
1	1265	503
2	5001	495

prune212.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes207.0ms

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	11
1	13	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

708.0ms	1544×	body	1280	valid
335.0ms	1205×	body	640	valid
245.0ms	4307×	body	80	valid
117.0ms	621×	body	320	valid
42.0ms	323×	body	160	valid