Details

Time bar (total: 24.8s)

sample301.0ms

Algorithm
intervals
Results
158.0ms102×body1280valid
54.0ms24×body2560valid
49.0ms66×body640valid
12.0ms26×body320valid
5.0ms30×body80valid
2.0ms8×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize10.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (tan (+ x eps)) (tan x))
3.6b
(tan (+ x eps))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×tan-quot add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u tan-sum frac-sub add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
52.0ms
(- (tan (+ x eps)) (tan x))
7.0ms
(tan (+ x eps))

series235.0ms

Counts
2 → 6
Calls
2 calls:
157.0ms
(- (tan (+ x eps)) (tan x))
77.0ms
(tan (+ x eps))

simplify1.3s

Counts
47 → 47
Iterations

Useful iterations: done (1.3s)

IterNodesCost
094720
1202600
2741510
done5001450

prune202.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.9b

localize30.0ms

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))
3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
73×add-sqr-sqrt
66×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
9×tan-quot
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1 flip3-- flip--
5×div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-def associate-*r* associate-*l* associate-/r* associate-/l/
2×flip3-+ frac-add 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 distribute-lft-out-- unswap-sqr
Counts
4 → 169
Calls
4 calls:
9.0ms
(+ (tan x) (tan eps))
46.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
16.0ms
(* (tan x) (tan eps))
163.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
143.0ms
(+ (tan x) (tan eps))
326.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
127.0ms
(* (tan x) (tan eps))
538.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.2s

Counts
181 → 181
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02404762
15963988
228923557
done50003556

prune645.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.3b
(pow (* (tan x) (tan eps)) 3)
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.1b
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
40×tan-quot
21×add-exp-log add-cbrt-cube
19×frac-times pow-prod-down
13×associate-*r/ associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u associate-*r* associate-*l* pow-sqr pow-prod-up log1p-expm1-u add-log-exp
3×cube-div pow-unpow
2×pow-pow pow-plus pow-exp *-commutative rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod swap-sqr fma-udef unswap-sqr sqr-pow
Counts
4 → 111
Calls
4 calls:
31.0ms
(* (tan x) (tan eps))
25.0ms
(pow (* (tan x) (tan eps)) 3)
120.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

series2.0s

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (tan x) (tan eps))
177.0ms
(pow (* (tan x) (tan eps)) 3)
189.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.5s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

simplify559.0ms

Counts
123 → 123
Iterations

Useful iterations: done (554.0ms)

IterNodesCost
02342288
17911859
done50001620

prune784.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize125.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (* (cos x) (cos eps)) 3)
0.5b
(pow (* (cos x) (cos eps)) 3)
0.5b
(pow (* (cos x) (cos eps)) 3)
2.1b
(- (+ (fma (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin eps) 3) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))) (pow (cos eps) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (* (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
44×*-un-lft-identity
42×add-cube-cbrt
39×prod-diff
28×times-frac
13×pow1 add-exp-log add-cbrt-cube
9×pow-unpow add-log-exp
6×pow-pow pow-exp rem-cube-cbrt
4×expm1-log1p-u log1p-expm1-u
3×cube-div cube-mult pow-to-exp unpow-prod-down fma-neg unpow3 cube-prod pow-prod-down prod-exp cos-mult cbrt-unprod div-inv sqr-pow
2×diff-log frac-sub difference-of-squares
1×sub-neg flip3-- flip3-+ associate--l+ sum-log flip-- flip-+ distribute-lft-out--
Counts
4 → 138
Calls
4 calls:
9.0ms
(pow (* (cos x) (cos eps)) 3)
20.0ms
(pow (* (cos x) (cos eps)) 3)
19.0ms
(pow (* (cos x) (cos eps)) 3)
167.0ms
(- (+ (fma (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin eps) 3) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))) (pow (cos eps) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (* (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

series2.3s

Counts
4 → 12
Calls
4 calls:
80.0ms
(pow (* (cos x) (cos eps)) 3)
92.0ms
(pow (* (cos x) (cos eps)) 3)
111.0ms
(pow (* (cos x) (cos eps)) 3)
2.0s
(- (+ (fma (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin eps) 3) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))) (pow (cos eps) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (* (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (pow (sin x) 3) (pow (cos x) 3)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

simplify545.0ms

Counts
150 → 150
Iterations

Useful iterations: done (536.0ms)

IterNodesCost
028715253
186114511
done500012291

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

regimes206.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046169
159169
done59169

end0.0ms

sample9.7s

Algorithm
intervals
Results
5.1s3336×body1280valid
1.6s1843×body640valid
1.6s654×body2560valid
747.0ms767×body320valid
182.0ms1069×body80valid
92.0ms331×body160valid