Details

sample302.0ms

Algorithm

intervals

Results

28.0ms	60×	body	1280	valid
8.0ms	31×	body	640	valid
7.0ms	134×	body	80	valid
4.0ms	21×	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

Filtered

1 candidates to 0 candidates (0.0%)

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)))
0.2b	(* (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:

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))

series224.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
40.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune237.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ 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))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

12.0ms	(/ 1 (/ (+ 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))
5.0ms	(* (tan x) (tan x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
36.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify71.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	545	2150
1	2567	1968
2	5001	1866

prune274.0ms

Filtered

177 candidates to 91 candidates (51.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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))

rewrite45.0ms

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))
28.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (sqrt 1.0) (tan x))
102.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
37.0ms	(- (sqrt 1.0) (tan x))
35.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (40.0ms)

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

prune233.0ms

Filtered

101 candidates to 68 candidates (67.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

53.0ms	(* (log (exp (+ (sqrt 1.0) (tan x)))) (- (sqrt 1.0) (tan x)))
7.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))
13.0ms	(exp (+ (sqrt 1.0) (tan x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (log (exp (+ (sqrt 1.0) (tan x)))) (- (sqrt 1.0) (tan x)))
41.0ms	(- (sqrt 1.0) (tan x))
32.0ms	(* (tan x) (tan x))
66.0ms	(exp (+ (sqrt 1.0) (tan x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	300	663
1	1177	571
2	5001	550

prune241.0ms

Filtered

101 candidates to 65 candidates (64.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	20
1	20	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

709.0ms	1581×	body	1280	valid
336.0ms	1211×	body	640	valid
243.0ms	4327×	body	80	valid
113.0ms	600×	body	320	valid
36.0ms	281×	body	160	valid