Details

sample97.0ms

Algorithm

intervals

Results

48.0ms	107×	body	1280	valid
19.0ms	18×	body	2560	valid
12.0ms	51×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	40×	body	80	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
3.6b	(tan (+ x eps))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`tan-quot`
4×	`tan-sum`
3×	`frac-sub`
2×	`+-commutative`
1×	`sub-neg` `flip3--` `flip--`

Counts

2 → 10

Calls

2 calls:

4.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series135.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
48.0ms	(tan (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (20.0ms)

Iter	Nodes	Cost
0	121	140
1	255	140
2	645	138
3	2116	137
4	5001	137

prune40.0ms

Filtered

16 candidates to 10 candidates (62.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	12	4	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	4	17

Merged error: 14.6b

Counts

17 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan eps) (tan x))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`tan-quot`
6×	`frac-sub` `associate-/l/`
3×	`flip3-+` `frac-add` `flip-+`
2×	`flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`+-commutative` `frac-times` `sub-neg` `associate-r/` `associate-l/` `*-commutative` `div-inv`

Counts

4 → 26

Calls

4 calls:

6.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
3.0ms	(+ (tan x) (tan eps))
4.0ms	(* (tan eps) (tan x))
8.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series767.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
93.0ms	(+ (tan x) (tan eps))
92.0ms	(* (tan eps) (tan x))
370.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify36.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	307	501
1	1074	498
2	5001	484

prune151.0ms

Filtered

38 candidates to 33 candidates (86.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	25	13	38
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	29	13	42

Merged error: 14.4b

Counts

42 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan eps) (tan x))
0.3b	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b	(pow (* (tan eps) (tan x)) 3)
3.6b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

62×	`tan-quot`
30×	`frac-times`
20×	`frac-sub`
18×	`associate-*l/`
14×	`associate-*r/`
10×	`flip3-+` `flip-+`
9×	`associate-/l/`
8×	`associate--l+`
7×	`*-commutative`
4×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in`
3×	`frac-2neg` `frac-add` `clear-num`
2×	`unpow-prod-down` `swap-sqr` `associate-r` `associate-l`
1×	`pow2` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `flip--` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

4.0ms	(* (tan eps) (tan x))
8.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
3.0ms	(pow (* (tan eps) (tan x)) 3)
23.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (tan x))

series1.9s

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (tan eps) (tan x))
112.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
126.0ms	(pow (* (tan eps) (tan x)) 3)
1.5s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1092	2425
1	5002	2367

prune395.0ms

Filtered

76 candidates to 64 candidates (84.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 0.2b

Counts

89 → 8

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(pow (cos x) 3)
0.4b	(pow (cos x) 3)
2.2b	(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

rewrite20.8s

Algorithm

rewrite-expression-head

Rules

196110×	`frac-add`
100398×	`associate-/r*`
75271×	`frac-2neg` `clear-num`
68151×	`frac-sub`
59460×	`associate-/l*`
58995×	`frac-times`
55878×	`sqr-pow`
42360×	`associate-r`
31224×	`*-commutative`
24435×	`unpow2`
24273×	`unpow3`
14340×	`associate-l`
7170×	`unswap-sqr`
6555×	`associate-*r/`
2868×	`flip3-+` `flip-+`
2565×	`associate-*l/`
8×	`associate--l+`
6×	`associate-+l+`
4×	`+-commutative` `associate-+r+`
3×	`pow-to-exp`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`sub-neg` `flip3--` `flip--`

Counts

4 → 68172

Calls

4 calls:

2.0ms	(pow (cos x) 3)
2.0ms	(pow (cos x) 3)
2.0ms	(pow (cos x) 3)
5.9s	(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (cos x) 3)
26.0ms	(pow (cos x) 3)
26.0ms	(pow (cos x) 3)
1.2s	(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

simplify2.3m

Algorithm

egg-herbie

Counts

68184 → 68184

Iterations

Useful iterations: 0 (7.4s)

Iter	Nodes	Cost
0	382314	15661042

prune7.3m

Filtered: 68184 candidates to 68177 candidates (100.0%)