Details

sample176.0ms

Algorithm

intervals

Results

93.0ms	119×	body	1280	valid
28.0ms	15×	body	2560	valid
26.0ms	59×	body	640	valid
8.0ms	26×	body	320	valid
7.0ms	11×	body	160	valid
3.0ms	26×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(- (tan (+ x eps)) (tan x))
3.4b	(tan (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series146.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify81.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune90.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
1.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

12.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
45.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series759.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
93.0ms	(+ (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
360.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune276.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
6.0b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

13.0ms	(* (+ (tan x) (tan eps)) (cos x))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (+ (tan x) (tan eps)) (cos x))
93.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
213.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	527	955
1	2405	907
2	5002	907

prune364.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (sin x) 2) (sin eps))
0.2b	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
0.3b	(* (tan x) (tan eps))
0.3b	(pow (sin x) 2)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`prod-exp`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`div-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-r` `cbrt-unprod`
5×	`unswap-sqr`
4×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp` `add-log-exp`
3×	`pow-unpow` `unpow2` `sqr-pow`
2×	`*-commutative`
1×	`frac-times` `pow-pow` `frac-2neg` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `div-inv` `associate-/l`

Counts

4 → 92

Calls

4 calls:

7.0ms	(* (pow (sin x) 2) (sin eps))
6.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
5.0ms	(* (tan x) (tan eps))
2.0ms	(pow (sin x) 2)

series276.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (pow (sin x) 2) (sin eps))
104.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
95.0ms	(* (tan x) (tan eps))
20.0ms	(pow (sin x) 2)

simplify61.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	443	718
1	2027	593
2	5001	593

prune372.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes143.0ms

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	30	22
1	30	22

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.6s	3329×	body	1280	valid
1.1s	656×	body	2560	valid
820.0ms	1815×	body	640	valid
234.0ms	765×	body	320	valid
136.0ms	1106×	body	80	valid
71.0ms	329×	body	160	valid