Details

Time bar (total: 6.0s)

sample83.0ms

Algorithm
intervals
Results
42.0ms107×body1280valid
15.0ms18×body2560valid
10.0ms51×body640valid
4.0ms29×body320valid
2.0ms40×body80valid
1.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

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: 36.0b

Counts
2 → 1

localize9.0ms

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))

series140.0ms

Counts
2 → 6
Calls
2 calls:
91.0ms
(- (tan (+ x eps)) (tan x))
49.0ms
(tan (+ x eps))

simplify77.0ms

Algorithm
egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 3 (21.0ms)

IterNodesCost
0129138
1284136
2769136
32484134
45002134

prune36.0ms

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: 14.6b

Counts
17 → 4

localize12.0ms

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))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
16×tan-quot
6×frac-sub associate-/l/
4×associate-/r/
3×flip3-- flip3-+ fma-neg frac-add flip-- flip-+
2×frac-2neg clear-num div-inv
1×+-commutative frac-times sub-neg associate-*r/ associate-*l/ *-commutative
Counts
4 → 29
Calls
4 calls:
6.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
3.0ms
(+ (tan x) (tan eps))
3.0ms
(* (tan eps) (tan x))
9.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series809.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
96.0ms
(+ (tan x) (tan eps))
96.0ms
(* (tan eps) (tan x))
389.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify38.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0325500
11162494
25002479

prune182.0ms

Filtered
41 candidates to 36 candidates (87.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New291241
Fresh303
Picked011
Done000
Total321345

Merged error: 14.3b

Counts
45 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.1b
(/ 1 (- 1 (* (tan eps) (tan x))))
0.2b
(* (tan eps) (tan x))
3.7b
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan eps) (tan x)))) (- (tan x)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×tan-quot
2×associate-/r/
1×+-commutative frac-times flip3-- frac-2neg flip3-+ associate-*r/ associate-*l/ frac-add clear-num *-commutative flip-- flip-+ fma-udef div-inv inv-pow
Counts
4 → 15
Calls
4 calls:
3.0ms
(+ (tan x) (tan eps))
4.0ms
(/ 1 (- 1 (* (tan eps) (tan x))))
4.0ms
(* (tan eps) (tan x))
1.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan eps) (tan x)))) (- (tan x)))

series635.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(+ (tan x) (tan eps))
133.0ms
(/ 1 (- 1 (* (tan eps) (tan x))))
98.0ms
(* (tan eps) (tan x))
308.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan eps) (tan x)))) (- (tan x)))

simplify74.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0212207
1702204
22722204
35001201

prune129.0ms

Filtered
27 candidates to 22 candidates (81.5%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New25227
Fresh11011
Picked101
Done011
Total271340

Merged error: 14.3b

Counts
40 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (tan x) (tan eps) (- 1))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (- 1) (fma (tan x) (tan eps) (- 1)))
3.7b
(fma (+ (tan x) (tan eps)) (/ (- 1) (fma (tan x) (tan eps) (- 1))) (- (tan x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
2×tan-quot fma-udef
1×+-commutative neg-sub0 neg-mul-1 frac-2neg flip3-+ div-sub distribute-frac-neg frac-add clear-num flip-+ div-inv associate-/l*
Counts
4 → 12
Calls
4 calls:
1.0ms
(fma (tan x) (tan eps) (- 1))
3.0ms
(+ (tan x) (tan eps))
3.0ms
(/ (- 1) (fma (tan x) (tan eps) (- 1)))
1.0ms
(fma (+ (tan x) (tan eps)) (/ (- 1) (fma (tan x) (tan eps) (- 1))) (- (tan x)))

series659.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(fma (tan x) (tan eps) (- 1))
99.0ms
(+ (tan x) (tan eps))
139.0ms
(/ (- 1) (fma (tan x) (tan eps) (- 1)))
309.0ms
(fma (+ (tan x) (tan eps)) (/ (- 1) (fma (tan x) (tan eps) (- 1))) (- (tan x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0166202
1417199
21355197
35002194

prune131.0ms

Filtered
24 candidates to 19 candidates (79.2%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New23124
Fresh11011
Picked011
Done011
Total241337

Merged error: 14.3b

Counts
37 → 13

regimes148.0ms

Accuracy

84.2% (1.1b remaining)

Error of 15.5b against oracle of 14.3b and baseline of 21.6b

bsearch47.0ms

Steps
ItersRangePoint
4
1.2424293569324924e-77
1.7367894335539448e-77
1.4719210203796444e-77
3
-8.936037306675809e-91
-7.192882265974599e-91
-8.827090116631984e-91

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04034
14034

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s3328×body1280valid
555.0ms635×body2560valid
398.0ms1825×body640valid
111.0ms769×body320valid
48.0ms1096×body80valid
33.0ms347×body160valid