Details

Time bar (total: 9.6s)

sample155.0ms

Algorithm
intervals
Results
69.0ms97×body1280valid
37.0ms22×body2560valid
27.0ms69×body640valid
5.0ms20×body320valid
3.0ms39×body80valid
2.0ms9×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize14.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (tan (+ x eps)) (tan x))
3.0b
(tan (+ x eps))

rewrite26.0ms

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:
17.0ms
(- (tan (+ x eps)) (tan x))
8.0ms
(tan (+ x eps))

series152.0ms

Counts
2 → 6
Calls
2 calls:
93.0ms
(- (tan (+ x eps)) (tan x))
59.0ms
(tan (+ x eps))

simplify83.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (23.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune86.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.3b
(* (tan x) (tan eps))
2.0b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite140.0ms

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))
30.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
17.0ms
(* (tan x) (tan eps))
83.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series824.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(+ (tan x) (tan eps))
233.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
101.0ms
(* (tan x) (tan eps))
389.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify43.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03971050
114321005
25001995

prune281.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (cos x))
0.2b
(* (sin x) (sin eps))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
6.8b
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite498.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×add-exp-log add-cbrt-cube
16×*-un-lft-identity
14×add-cube-cbrt
11×times-frac
6×pow1 add-log-exp
5×cbrt-undiv div-exp prod-exp cbrt-unprod
4×associate-/r* associate-/l*
3×associate-*r* associate-*l*
2×frac-2neg clear-num div-inv sin-mult difference-of-squares
1×tan-quot sub-neg quot-tan flip3-- diff-log pow-prod-down associate-/r/ cos-mult *-commutative frac-sub flip-- associate-/l/ distribute-lft-out-- unswap-sqr
Counts
4 → 86
Calls
4 calls:
9.0ms
(/ (sin x) (cos x))
13.0ms
(* (sin x) (sin eps))
19.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
456.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series599.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (sin x) (cos x))
47.0ms
(* (sin x) (sin eps))
105.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
426.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify60.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04361100
11928960
25002960

prune381.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (tan x) (tan eps)) (cos x))
0.3b
(* (tan x) (tan eps))
0.3b
(* (tan x) (tan eps))
7.6b
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
17×associate-*l/
16×add-sqr-sqrt
14×tan-quot
12×*-un-lft-identity
10×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
9×associate-*r*
6×frac-sub add-log-exp
4×flip3-- flip--
3×flip3-+ pow-prod-down frac-add prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
2×frac-times associate-*r/
1×sub-neg diff-log distribute-lft-out
Counts
4 → 82
Calls
4 calls:
30.0ms
(* (+ (tan x) (tan eps)) (cos x))
18.0ms
(* (tan x) (tan eps))
15.0ms
(* (tan x) (tan eps))
34.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (+ (tan x) (tan eps)) (cos x))
102.0ms
(* (tan x) (tan eps))
100.0ms
(* (tan x) (tan eps))
224.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify74.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0527955
12405907
25002907

prune338.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

regimes106.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
12921

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.4s3234×body1280valid
1.1s653×body2560valid
821.0ms1898×body640valid
213.0ms778×body320valid
94.0ms1115×body80valid
66.0ms322×body160valid