Details

Time bar (total: 28.3s)

sample266.0ms

Algorithm
intervals
Results
124.0ms96×body1280valid
59.0ms24×body2560valid
39.0ms56×body640valid
19.0ms39×body320valid
4.0ms31×body80valid
3.0ms10×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: 36.1b

localize11.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (tan (+ x eps)) (tan x))
6.3b
(tan (+ x eps))

rewrite77.0ms

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:
30.0ms
(- (tan (+ x eps)) (tan x))
46.0ms
(tan (+ x eps))

series210.0ms

Counts
2 → 6
Calls
2 calls:
135.0ms
(- (tan (+ x eps)) (tan x))
75.0ms
(tan (+ x eps))

simplify2.4s

Counts
47 → 47
Iterations

Useful iterations: done (2.4s)

IterNodesCost
094720
1194597
2457510
31461450
done5000438

prune191.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.0b

localize13.0ms

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))
0.2b
(* (tan x) (tan eps))
2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite228.0ms

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:
43.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
10.0ms
(+ (tan x) (tan eps))
30.0ms
(* (tan x) (tan eps))
128.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
324.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
135.0ms
(+ (tan x) (tan eps))
137.0ms
(* (tan x) (tan eps))
591.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.5s

Counts
181 → 181
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02404762
15603970
215583555
done50003149

prune486.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(pow (* (tan x) (tan eps)) 3)
2.4b
(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)))

rewrite123.0ms

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:
16.0ms
(* (tan x) (tan eps))
89.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
14.0ms
(pow (* (tan x) (tan eps)) 3)
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)))

series1.7s

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (tan x) (tan eps))
167.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
161.0ms
(pow (* (tan x) (tan eps)) 3)
1.2s
(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)))

simplify2.2s

Counts
123 → 123
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02342288
16581831
229631614
done50021583

prune610.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.1b

localize116.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (/ (sin x) (cos x)) 3)
0.4b
(pow (cos eps) 3)
0.4b
(pow (sin eps) 3)
2.5b
(- (fma (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin eps) 3) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (+ (fma (/ (/ (pow (sin eps) 2) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (pow (cos eps) 2)) (+ (pow (/ (sin x) (cos x)) 3) (/ (sin x) (cos x))) (/ (sin x) (* (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3)) (cos x)))) (/ (/ (sin eps) (cos eps)) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))))) (/ (sin x) (cos x)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
62×*-un-lft-identity
60×add-cube-cbrt
46×times-frac
39×prod-diff
19×unpow-prod-down cube-prod
9×add-exp-log pow-unpow add-cbrt-cube
7×pow1
6×add-log-exp
5×div-inv
4×expm1-log1p-u pow-exp log1p-expm1-u rem-cube-cbrt
3×cube-mult pow-to-exp pow-pow fma-neg unpow3 sqr-pow
2×difference-of-squares
1×cbrt-undiv cube-div sub-neg flip3-- diff-log div-exp associate--l+ flip-- fma-udef distribute-lft-out--
Counts
4 → 158
Calls
4 calls:
13.0ms
(pow (/ (sin x) (cos x)) 3)
11.0ms
(pow (cos eps) 3)
8.0ms
(pow (sin eps) 3)
33.0ms
(- (fma (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin eps) 3) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (+ (fma (/ (/ (pow (sin eps) 2) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (pow (cos eps) 2)) (+ (pow (/ (sin x) (cos x)) 3) (/ (sin x) (cos x))) (/ (sin x) (* (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3)) (cos x)))) (/ (/ (sin eps) (cos eps)) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))))) (/ (sin x) (cos x)))

series2.0s

Counts
4 → 12
Calls
4 calls:
62.0ms
(pow (/ (sin x) (cos x)) 3)
31.0ms
(pow (cos eps) 3)
33.0ms
(pow (sin eps) 3)
1.8s
(- (fma (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin eps) 3) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (+ (fma (/ (/ (pow (sin eps) 2) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (pow (cos eps) 2)) (+ (pow (/ (sin x) (cos x)) 3) (/ (sin x) (cos x))) (/ (sin x) (* (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3)) (cos x)))) (/ (/ (sin eps) (cos eps)) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))))) (/ (sin x) (cos x)))

simplify2.4s

Counts
170 → 170
Iterations

Useful iterations: done (2.4s)

IterNodesCost
034315704
193815104
2376012238
done500112234

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

regimes343.0ms

Accuracy

92.6% (1.1b remaining)

Error of 6.1b against oracle of 5.0b and baseline of 19.7b

bsearch275.0ms

Steps
ItersRangePoint
11
1.1123901126486127e-34
1.9762467893330864e-06
1.3424092820004812e-20
5
-2.9278891142885936e-51
-1.3141126890030885e-51
-2.692188506596357e-51

simplify9.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
070262
187256
done87256

end0.0ms

sample10.6s

Algorithm
intervals
Results
4.8s3277×body1280valid
2.1s1781×body640valid
1.7s640×body2560valid
887.0ms834×body320valid
598.0ms1104×body80valid
194.0ms364×body160valid