Details

Time bar (total: 10.1s)

sample2.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results
45.0ms116×body1280valid
22.0ms25×body2560valid
13.0ms56×body640valid
4.0ms27×body320valid
1.0ms23×body80valid
1.0ms9×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: 39.9b

Counts
2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

1.5b
(- (tan (+ x eps)) (tan x))
3.9b
(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))

series40.0ms

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

simplify76.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (21.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune67.0ms

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: 16.7b

Counts
32 → 8

localize12.0ms

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))
3.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite31.0ms

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:
7.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms
(+ (tan x) (tan eps))
7.0ms
(* (tan x) (tan eps))
11.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series198.0ms

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))
100.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify45.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03971052
114321007
25001995

prune193.0ms

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

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New831598
Fresh347
Picked101
Done000
Total8719106

Merged error: 16.6b

Counts
106 → 19

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.2b
(* (sin x) (sin eps))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
10×*-un-lft-identity
8×add-log-exp
6×pow1 add-cube-cbrt
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×tan-quot associate-*r* associate-*l*
2×times-frac sin-mult difference-of-squares
1×+-commutative sub-neg flip3-- frac-2neg flip3-+ diff-log pow-prod-down frac-add clear-num associate-/r* sum-log associate-/r/ cos-mult *-commutative frac-sub flip-- flip-+ div-inv associate-/l/ distribute-lft-out associate-/l* distribute-lft-out-- unswap-sqr
Counts
4 → 71
Calls
4 calls:
4.0ms
(+ (tan x) (tan eps))
4.0ms
(* (sin x) (sin eps))
7.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
17.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series155.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (tan x) (tan eps))
9.0ms
(* (sin x) (sin eps))
22.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
101.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify47.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0427917
11787792
25001792

prune151.0ms

Filtered
59 candidates to 83 candidates (-40.7%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New79483
Fresh41418
Picked101
Done000
Total8418102

Merged error: 16.6b

Counts
102 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.4b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
45×tan-quot
21×frac-times
20×add-exp-log add-cbrt-cube
19×pow-prod-down
15×associate-*r/
14×associate-*l/
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×add-cube-cbrt *-un-lft-identity
7×associate-*r* associate-*l*
6×add-log-exp
5×frac-sub
4×pow-sqr pow-prod-up
3×*-commutative
2×flip3-+ pow-plus associate--l+ flip-+ unswap-sqr
1×pow2 distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log swap-sqr flip--
Counts
4 → 110
Calls
4 calls:
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
11.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
11.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series392.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (tan x) (tan eps))
24.0ms
(* (tan x) (tan eps))
30.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
317.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify82.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05991352
130211220
250011220

prune116.0ms

Filtered
75 candidates to 122 candidates (-62.7%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1193122
Fresh11617
Picked101
Done000
Total12119140

Merged error: 16.6b

Counts
140 → 19

regimes253.0ms

Accuracy

82.7% (1.3b remaining)

Error of 16.1b against oracle of 14.8b and baseline of 22.2b

bsearch134.0ms

Steps
ItersRangePoint
9
7.437548361328832e-20
5.3867791207833144e-11
2.69577026480216e-19
10
-1.2496252390790465e-116
-2.308702529949821e-129
-1.2364989517645001e-116

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04256
14256

end0.0ms

sample5.4s

Algorithm
intervals
sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results
1.3s3328×body1280valid
580.0ms662×body2560valid
404.0ms1795×body640valid
116.0ms769×body320valid
51.0ms1099×body80valid
36.0ms347×body160valid

Profiling

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