Details

Time bar (total: 9.9s)

sample166.0ms

Algorithm
intervals
Results
69.0ms95×body1280valid
47.0ms28×body2560valid
23.0ms54×body640valid
11.0ms30×body320valid
3.0ms36×body80valid
2.0ms13×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize9.0ms

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))
3.0ms
(tan (+ x eps))

series142.0ms

Counts
2 → 6
Calls
2 calls:
88.0ms
(- (tan (+ x eps)) (tan x))
54.0ms
(tan (+ x eps))

simplify76.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune86.0ms

Filtered
31 candidates to 25 candidates (80.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.3b

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))
0.3b
(* (tan x) (tan eps))
3.5b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite59.0ms

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:
11.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
38.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series756.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
92.0ms
(+ (tan x) (tan eps))
93.0ms
(* (tan x) (tan eps))
353.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03971052
114321007
25001996

prune284.0ms

Filtered
98 candidates to 74 candidates (75.5%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (sin eps))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.5b
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
11×*-un-lft-identity
9×prod-exp cbrt-unprod add-log-exp
8×cbrt-undiv div-exp
6×pow1 add-cube-cbrt
3×times-frac associate-*r* associate-*l* frac-sub sin-mult
2×frac-2neg diff-log clear-num associate-/r* associate-/r/ cos-mult div-inv associate-/l/ associate-/l* distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip3-+ pow-prod-down frac-add associate--l+ sum-log *-commutative flip-- flip-+ distribute-lft-out unswap-sqr
Counts
4 → 86
Calls
4 calls:
4.0ms
(* (sin x) (sin eps))
6.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
5.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
241.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin x) (sin eps))
99.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
99.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
372.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify64.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04641846
122151611
250011611

prune380.0ms

Filtered
98 candidates to 66 candidates (67.3%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.0b
(log (exp (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
3.5b
(- (+ (/ (sin x) (* (- 1 (log (exp (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite378.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log add-cbrt-cube
11×add-sqr-sqrt *-un-lft-identity
9×add-log-exp
8×cbrt-undiv div-exp prod-exp cbrt-unprod
7×log-pow
6×add-cube-cbrt exp-prod
5×pow1
4×log-prod times-frac associate-/r/ cos-mult
3×frac-sub div-inv
2×frac-2neg diff-log clear-num associate-/r* associate-/l/ sin-mult associate-/l* distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip3-+ rem-log-exp frac-add associate--l+ sum-log flip-- flip-+ exp-lft-sqr distribute-lft-out
Counts
4 → 86
Calls
4 calls:
7.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
5.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
5.0ms
(log (exp (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
357.0ms
(- (+ (/ (sin x) (* (- 1 (log (exp (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series667.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
98.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
101.0ms
(log (exp (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
370.0ms
(- (+ (/ (sin x) (* (- 1 (log (exp (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04832042
121241772
250011772

prune372.0ms

Filtered
98 candidates to 66 candidates (67.3%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.1b

regimes215.0ms

Accuracy

90.4% (0.8b remaining)

Error of 15.2b against oracle of 14.4b and baseline of 22.3b

bsearch162.0ms

Steps
ItersRangePoint
10
2.333660012862611e-22
2.8376047635535897e-09
7.737989198753307e-19
7
-3.911354777868884e-16
-2.814616726593186e-18
-3.9980652276674155e-18

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03522
13522

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.5s3282×body1280valid
1.1s630×body2560valid
818.0ms1841×body640valid
243.0ms767×body320valid
106.0ms1138×body80valid
66.0ms342×body160valid