Details

Time bar (total: 9.0s)

sample82.0ms

Algorithm
intervals
Results
39.0ms112×body1280valid
18.0ms21×body2560valid
13.0ms59×body640valid
2.0ms18×body320valid
1.0ms35×body80valid
1.0ms11×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: 37.5b

Counts
2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (tan (+ x eps)) (tan x))
3.8b
(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))
3.0ms
(tan (+ x eps))

series135.0ms

Counts
2 → 6
Calls
2 calls:
87.0ms
(- (tan (+ x eps)) (tan x))
48.0ms
(tan (+ x eps))

simplify75.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune77.0ms

Filtered
31 candidates to 25 candidates (80.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New24731
Fresh000
Picked101
Done000
Total25732

Merged error: 14.6b

Counts
32 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
2.2b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite30.0ms

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

series734.0ms

Counts
4 → 12
Calls
4 calls:
210.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
90.0ms
(+ (tan x) (tan eps))
89.0ms
(* (tan x) (tan eps))
344.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify49.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03971050
114321005
25001995

prune270.0ms

Filtered
98 candidates to 74 candidates (75.5%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New841498
Fresh426
Picked101
Done000
Total8916105

Merged error: 14.4b

Counts
105 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.3b
(pow (* (tan x) (tan eps)) 3)
2.2b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
17×tan-quot
13×add-sqr-sqrt
11×pow1 add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×associate-*r* associate-*l* add-log-exp
5×frac-times associate-*r/ frac-sub
4×associate-*l/
3×cube-div pow-unpow pow-prod-down prod-exp cbrt-unprod
2×pow-pow flip3-+ pow-exp associate--l+ *-commutative flip-+ rem-cube-cbrt unswap-sqr
1×distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- distribute-lft-in diff-log unpow3 cube-prod flip-- sqr-pow
Counts
4 → 86
Calls
4 calls:
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
5.0ms
(pow (* (tan x) (tan eps)) 3)
19.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series1.9s

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (tan x) (tan eps))
93.0ms
(* (tan x) (tan eps))
125.0ms
(pow (* (tan x) (tan eps)) 3)
1.6s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify112.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
06751557
136431326
250031326

prune348.0ms

Filtered
98 candidates to 73 candidates (74.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New94498
Fresh9615
Picked101
Done000
Total10410114

Merged error: 0.3b

Counts
114 → 10

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin x) 3)
0.4b
(pow (sin x) 3)
0.4b
(pow (sin x) 3)
2.0b
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity frac-add
13×add-cube-cbrt add-log-exp
11×frac-sub
9×unpow-prod-down pow-unpow cube-prod
7×pow1 add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×cube-mult frac-times pow-to-exp pow-pow diff-log unpow3 associate-*r/ pow-exp sum-log rem-cube-cbrt sqr-pow
2×distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- times-frac associate-*l/ associate--l+ flip-- distribute-lft-out
Counts
4 → 99
Calls
4 calls:
3.0ms
(pow (sin x) 3)
3.0ms
(pow (sin x) 3)
3.0ms
(pow (sin x) 3)
37.0ms
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

series1.4s

Counts
4 → 12
Calls
4 calls:
31.0ms
(pow (sin x) 3)
30.0ms
(pow (sin x) 3)
36.0ms
(pow (sin x) 3)
1.3s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

simplify77.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
010145753
150015543

prune806.0ms

Filtered
111 candidates to 69 candidates (62.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1083111
Fresh189
Picked101
Done000
Total11011121

Merged error: 0.1b

Counts
121 → 11

regimes182.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061113
163113
263113

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.2s3237×body1280valid
532.0ms620×body2560valid
391.0ms1872×body640valid
106.0ms779×body320valid
46.0ms1133×body80valid
32.0ms359×body160valid