Details

Time bar (total: 7.2s)

sample84.0ms

Algorithm
intervals
Results
42.0ms102×body1280valid
15.0ms18×body2560valid
13.0ms63×body640valid
3.0ms21×body320valid
2.0ms45×body80valid
1.0ms7×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: 33.3b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (tan (+ x eps)) (tan x))
2.6b
(tan (+ x eps))

rewrite10.0ms

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:
6.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series138.0ms

Counts
2 → 6
Calls
2 calls:
90.0ms
(- (tan (+ x eps)) (tan x))
48.0ms
(tan (+ x eps))

simplify78.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (24.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune92.0ms

Filtered
31 candidates to 25 candidates (80.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New23831
Fresh000
Picked101
Done000
Total24832

Merged error: 15.6b

Counts
32 → 8

localize11.0ms

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))
0.2b
(* (tan x) (tan eps))
1.9b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

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:
8.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
12.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series750.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
92.0ms
(+ (tan x) (tan eps))
92.0ms
(* (tan x) (tan eps))
354.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify52.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03971050
114321005
25001994

prune264.0ms

Filtered
98 candidates to 74 candidates (75.5%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New871198
Fresh437
Picked101
Done000
Total9214106

Merged error: 15.5b

Counts
106 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
4.8b
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
104×*-un-lft-identity
83×add-sqr-sqrt
67×add-cube-cbrt
23×associate-/r*
19×add-exp-log
16×associate-/r/ distribute-lft-out
15×tan-quot
13×add-cbrt-cube
8×div-exp
7×pow1 div-inv
6×associate-/l* add-log-exp
5×flip3-+ frac-add flip-+ difference-of-squares
4×cbrt-undiv
3×associate-*r* associate-*l*
2×rec-exp flip3-- frac-2neg 1-exp clear-num flip-- associate-/l/ distribute-lft-out--
1×frac-times sub-neg pow-flip diff-log div-sub associate-*r/ pow-prod-down associate-*l/ prod-exp *-commutative frac-sub cbrt-unprod inv-pow unswap-sqr
Counts
4 → 178
Calls
4 calls:
5.0ms
(* (tan x) (tan eps))
8.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
10.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
27.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series950.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (tan x) (tan eps))
270.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
220.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
365.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify86.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07032791
132942506
250012503

prune358.0ms

Filtered
190 candidates to 105 candidates (55.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1819190
Fresh7613
Picked101
Done000
Total18915204

Merged error: 15.5b

Counts
204 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt add-log-exp
6×pow1
5×tan-quot associate-/r/
4×prod-exp cbrt-unprod
3×cbrt-undiv frac-times flip3-- times-frac div-exp associate-*r* associate-*l* associate-*l/ cos-mult flip-- associate-/l*
2×flip3-+ associate-*r/ flip-+ associate-/l/
1×+-commutative sub-neg frac-2neg diff-log pow-prod-down clear-num associate-/r* sum-log *-commutative frac-sub div-inv distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 77
Calls
4 calls:
6.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
5.0ms
(* (tan x) (tan eps))
17.0ms
(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
14.0ms
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

series833.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
92.0ms
(* (tan x) (tan eps))
279.0ms
(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
370.0ms
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

simplify66.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05691467
123231312
250031312

prune309.0ms

Filtered
89 candidates to 69 candidates (77.5%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New85489
Fresh11314
Picked101
Done000
Total8717104

Merged error: 15.5b

Counts
104 → 17

regimes196.0ms

Accuracy

85% (1.1b remaining)

Error of 15.5b against oracle of 14.4b and baseline of 21.7b

bsearch109.0ms

Steps
ItersRangePoint
7
4.257188695836942e-114
3.5333463215819873e-112
3.4814586759764392e-112
7
-1.6307236291024458e-15
-1.1642175043144516e-17
-2.2212137676965008e-17

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04542
14542

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s3348×body1280valid
527.0ms603×body2560valid
406.0ms1847×body640valid
107.0ms750×body320valid
49.0ms1122×body80valid
32.0ms330×body160valid

Profiling

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