Details

Time bar (total: 10.3s)

sample166.0ms

Algorithm
intervals
Results
84.0ms111×body1280valid
39.0ms24×body2560valid
22.0ms55×body640valid
8.0ms32×body320valid
2.0ms26×body80valid
1.0ms8×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: 39.7b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b
(- (tan (+ x eps)) (tan x))
4.0b
(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))

series135.0ms

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

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

localize10.0ms

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))))
0.2b
(* (tan x) (tan eps))
2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite64.0ms

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:
3.0ms
(+ (tan x) (tan eps))
11.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms
(* (tan x) (tan eps))
43.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series785.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(+ (tan x) (tan eps))
206.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
88.0ms
(* (tan x) (tan eps))
396.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify47.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03971050
114321005
25001995

prune326.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.6b
(- (+ (/ (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)))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
33×add-exp-log add-cbrt-cube
11×add-sqr-sqrt *-un-lft-identity
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod add-log-exp
6×add-cube-cbrt times-frac
5×associate-/l*
4×pow1 associate-/r/
3×frac-2neg clear-num associate-/r* frac-sub div-inv
2×flip3-- diff-log associate-*l/ cos-mult flip-- associate-/l/ sin-mult distribute-lft-out-- difference-of-squares
1×sub-neg flip3-+ frac-add associate--l+ sum-log flip-+ distribute-lft-out
Counts
4 → 90
Calls
4 calls:
11.0ms
(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
6.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
6.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
245.0ms
(- (+ (/ (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)))

series740.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
98.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
97.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
396.0ms
(- (+ (/ (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)))

simplify68.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05462112
124121871
250011871

prune391.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b
(/ (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.3b
(/ 1 (/ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
2.6b
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ 1 (/ (* (cos x) (cos eps)) (* (sin x) (sin eps))))) (cos eps)))) (/ (sin x) (cos x)))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
72×add-exp-log
46×add-cbrt-cube
30×div-exp
25×times-frac
20×add-sqr-sqrt *-un-lft-identity prod-exp
17×cbrt-undiv
15×add-cube-cbrt
12×cbrt-unprod
9×add-log-exp
8×associate-/r*
7×associate-/r/ div-inv
6×sin-mult
5×pow1 rec-exp 1-exp associate-/l*
3×frac-2neg clear-num frac-sub
2×diff-log cos-mult associate-/l/ distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- pow-flip flip3-+ frac-add associate--l+ sum-log flip-- flip-+ distribute-lft-out inv-pow
Counts
4 → 127
Calls
4 calls:
6.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
6.0ms
(/ (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms
(/ 1 (/ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
246.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ 1 (/ (* (cos x) (cos eps)) (* (sin x) (sin eps))))) (cos eps)))) (/ (sin x) (cos x)))

series668.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
100.0ms
(/ (* (cos x) (cos eps)) (* (sin x) (sin eps)))
100.0ms
(/ 1 (/ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
369.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ 1 (/ (* (cos x) (cos eps)) (* (sin x) (sin eps))))) (cos eps)))) (/ (sin x) (cos x)))

simplify102.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07262523
138292156
250012123

prune384.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.1b

regimes233.0ms

Accuracy

89.2% (0.8b remaining)

Error of 15.5b against oracle of 14.6b and baseline of 22.3b

bsearch205.0ms

Steps
ItersRangePoint
11
2.28145452431431e-18
2231369.5462890854
2.855628566329288e-18
10
-4.161461817671002e-38
-2.4684106388071866e-48
-1.9500134694671836e-38

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03923
13923

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.5s3341×body1280valid
1.1s666×body2560valid
965.0ms1788×body640valid
212.0ms779×body320valid
95.0ms1078×body80valid
76.0ms348×body160valid