Details

Time bar (total: 4.4s)

sample88.0ms

Algorithm
intervals
Results
43.0ms115×body1280valid
14.0ms17×body2560valid
12.0ms60×body640valid
3.0ms22×body320valid
1.0ms31×body80valid
1.0ms11×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.1b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (tan (+ x eps)) (tan x))
2.9b
(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))
4.0ms
(tan (+ x eps))

series38.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(- (tan (+ x eps)) (tan x))
15.0ms
(tan (+ x eps))

simplify75.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (21.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune61.0ms

Filtered
25 candidates to 31 candidates (-24.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New23831
Fresh000
Picked101
Done000
Total24832

Merged error: 12.4b

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))
2.8b
(- (/ (+ (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))))
4.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
13.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series197.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
20.0ms
(+ (tan x) (tan eps))
21.0ms
(* (tan x) (tan eps))
99.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03971050
114321005
25001994

prune156.0ms

Filtered
74 candidates to 98 candidates (-32.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New861298
Fresh527
Picked101
Done000
Total9214106

Merged error: 12.3b

Counts
106 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (tan x))
0.5b
(cbrt (tan x))
0.5b
(* (cbrt (tan x)) (cbrt (tan x)))
2.8b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×cbrt-prod
16×*-un-lft-identity
14×add-cube-cbrt
11×pow1
8×pow1/3
7×tan-quot
6×add-exp-log cbrt-div swap-sqr associate-*r* associate-*l* add-log-exp
4×add-cbrt-cube unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up difference-of-squares
1×pow2 frac-times sub-neg flip3-- times-frac pow-plus diff-log associate-*r/ associate-*l/ prod-exp *-commutative frac-sub flip-- cbrt-unprod distribute-lft-out--
Counts
4 → 83
Calls
4 calls:
2.0ms
(cbrt (tan x))
2.0ms
(cbrt (tan x))
7.0ms
(* (cbrt (tan x)) (cbrt (tan x)))
13.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))

series181.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(cbrt (tan x))
24.0ms
(cbrt (tan x))
33.0ms
(* (cbrt (tan x)) (cbrt (tan x)))
97.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))

simplify136.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
0315996
1971927
24325843
35002839

prune135.0ms

Filtered
68 candidates to 95 candidates (-39.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New92395
Fresh4913
Picked101
Done000
Total9712109

Merged error: 11.4b

Counts
109 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (* (neg (pow (cbrt (tan x)) 3)) (tan eps)))
0.5b
(cbrt (tan x))
0.8b
(pow (cbrt (tan x)) 3)
7.9b
(- (* (+ (tan x) (tan eps)) (cos x)) (sin x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log
9×cbrt-prod add-cbrt-cube
6×tan-quot unpow-prod-down cube-prod add-log-exp
4×cbrt-div associate-*r/
3×cube-div pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×pow-pow pow1/3 distribute-neg-frac
1×distribute-lft-neg-out cube-mult frac-times pow-to-exp sub-neg flip3-- diff-log unpow3 associate-*r* associate-*l/ pow-exp *-commutative distribute-rgt-neg-out flip-- rem-cube-cbrt sqr-pow
Counts
4 → 77
Calls
4 calls:
10.0ms
(* (sin x) (* (neg (pow (cbrt (tan x)) 3)) (tan eps)))
2.0ms
(cbrt (tan x))
4.0ms
(pow (cbrt (tan x)) 3)
8.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (sin x))

series115.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (sin x) (* (neg (pow (cbrt (tan x)) 3)) (tan eps)))
25.0ms
(cbrt (tan x))
36.0ms
(pow (cbrt (tan x)) 3)
25.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (sin x))

simplify67.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0450619
12302536
25001532

prune129.0ms

Filtered
58 candidates to 89 candidates (-53.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New86389
Fresh6511
Picked101
Done000
Total938101

Merged error: 0.2b

Counts
101 → 8

regimes122.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03323
14523
26023
36223
46223

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.3s3372×body1280valid
488.0ms573×body2560valid
394.0ms1838×body640valid
111.0ms778×body320valid
46.0ms1087×body80valid
33.0ms352×body160valid

Profiling

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