Details

Time bar (total: 6.8s)

sample81.0ms

Algorithm
intervals
Results
42.0ms112×body1280valid
13.0ms16×body2560valid
12.0ms58×body640valid
4.0ms27×body320valid
1.0ms35×body80valid
1.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.2b

Counts
2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b
(- (tan (+ x eps)) (tan x))
4.0b
(tan (+ x eps))

rewrite7.0ms

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))

series138.0ms

Counts
2 → 6
Calls
2 calls:
88.0ms
(- (tan (+ x eps)) (tan x))
49.0ms
(tan (+ x eps))

simplify72.0ms

Algorithm
egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 3 (20.0ms)

IterNodesCost
0121140
1255140
2645138
32116137
45001137

prune39.0ms

Filtered
16 candidates to 10 candidates (62.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New12416
Fresh000
Picked101
Done000
Total13417

Merged error: 14.9b

Counts
17 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.2b
(+ (tan x) (tan eps))
0.2b
(* (tan eps) (tan x))
1.4b
(- (/ (+ (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))

series752.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
92.0ms
(+ (tan x) (tan eps))
89.0ms
(* (tan eps) (tan x))
358.0ms
(- (/ (+ (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)

IterNodesCost
0307501
11074498
25001484

prune160.0ms

Filtered
38 candidates to 33 candidates (86.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New251338
Fresh303
Picked101
Done000
Total291342

Merged error: 14.8b

Counts
42 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (tan eps) (sin x)) (cos x))
0.2b
(+ (tan x) (tan eps))
0.2b
(* (tan eps) (sin x))
1.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan eps) (sin x)) (cos x)))) (tan x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×tan-quot
6×frac-sub
4×associate-/l/
2×frac-2neg flip3-+ associate-*l/ frac-add clear-num *-commutative flip-+ associate-/l*
1×+-commutative sub-neg flip3-- flip-- div-inv
Counts
4 → 22
Calls
4 calls:
5.0ms
(/ (* (tan eps) (sin x)) (cos x))
3.0ms
(+ (tan x) (tan eps))
3.0ms
(* (tan eps) (sin x))
9.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan eps) (sin x)) (cos x)))) (tan x))

series641.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (* (tan eps) (sin x)) (cos x))
95.0ms
(+ (tan x) (tan eps))
65.0ms
(* (tan eps) (sin x))
383.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan eps) (sin x)) (cos x)))) (tan x))

simplify123.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0304462
11034458
24961442
35001442

prune156.0ms

Filtered
34 candidates to 26 candidates (76.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New28634
Fresh6612
Picked101
Done000
Total351247

Merged error: 14.8b

Counts
47 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan eps) (tan x))
0.2b
(* (tan eps) (tan x))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
1.4b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ 1 (* (tan eps) (tan x)))) (tan x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
66×tan-quot
31×frac-times
20×frac-sub
19×associate-*l/
15×associate-*r/
10×flip3-+ flip-+
9×associate-/l/
7×*-commutative
4×associate--l+
3×frac-2neg frac-add clear-num
2×+-commutative distribute-rgt-in distribute-lft-in swap-sqr associate-*r* associate-*l*
1×pow2 sub-neg flip3-- flip--
Counts
4 → 59
Calls
4 calls:
4.0ms
(* (tan eps) (tan x))
4.0ms
(* (tan eps) (tan x))
9.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
16.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ 1 (* (tan eps) (tan x)))) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (tan eps) (tan x))
96.0ms
(* (tan eps) (tan x))
117.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
934.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ 1 (* (tan eps) (tan x)))) (tan x))

simplify124.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08751710
146481626
250021626

prune280.0ms

Filtered
71 candidates to 59 candidates (83.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New63871
Fresh10111
Picked101
Done000
Total74983

Merged error: 12.8b

Counts
83 → 9

regimes131.0ms

Accuracy

67.2% (2.4b remaining)

Error of 14.5b against oracle of 12.1b and baseline of 19.5b

bsearch121.0ms

Steps
ItersRangePoint
8
1.185487053096793e-108
9.185000414034106e-105
9.008897623605655e-105
9
-2.601450563965851e-48
-5.066505781040529e-56
-3.664077099768491e-52

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03836
14236
24236

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s3361×body1280valid
523.0ms614×body2560valid
378.0ms1808×body640valid
106.0ms769×body320valid
46.0ms1093×body80valid
33.0ms355×body160valid