Details

Time bar (total: 28.5s)

sample153.0ms

Algorithm
intervals
Results
65.0ms93×body1280valid
43.0ms24×body2560valid
24.0ms62×body640valid
6.0ms23×body320valid
3.0ms39×body80valid
3.0ms15×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b
(tan (+ x eps))
2.4b
(- (tan (+ x eps)) (tan x))

rewrite13.0ms

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:
3.0ms
(tan (+ x eps))
9.0ms
(- (tan (+ x eps)) (tan x))

series144.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(tan (+ x eps))
92.0ms
(- (tan (+ x eps)) (tan x))

simplify1.2s

Counts
47 → 47
Iterations

Useful iterations: 3 (260.0ms)

IterNodesCost
094720
1199597
2544510
32312450
done5001450

prune121.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.8b

localize14.0ms

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))
3.7b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite77.0ms

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:
11.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
48.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series750.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
92.0ms
(+ (tan x) (tan eps))
91.0ms
(* (tan x) (tan eps))
355.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.0s

Counts
181 → 181
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02404762
15763970
219363549
done50003525

prune479.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(pow (* (tan x) (tan eps)) 3)
3.7b
(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)))

rewrite35.0ms

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:
5.0ms
(* (tan x) (tan eps))
22.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
4.0ms
(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)))

series1.3s

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (tan x) (tan eps))
122.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
130.0ms
(pow (* (tan x) (tan eps)) 3)
998.0ms
(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)))

simplify1.3s

Counts
123 → 123
Iterations

Useful iterations: 2 (309.0ms)

IterNodesCost
02342288
16861831
236121614
done50001614

prune543.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.6b

localize65.0ms

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)
3.8b
(- (+ (/ (/ (sin eps) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (cos eps)) (+ (* (/ (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)))) (fma (/ (pow (sin x) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (/ (pow (sin eps) 3) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))))) (/ (sin x) (cos x)))

rewrite11.4s

Algorithm
rewrite-expression-head
Rules
82×*-un-lft-identity
54×add-sqr-sqrt
52×prod-diff
49×add-cube-cbrt
37×times-frac
15×distribute-lft-out
13×pow1 add-exp-log add-cbrt-cube add-log-exp
9×pow-unpow
6×pow-pow pow-exp rem-cube-cbrt
4×expm1-log1p-u fma-neg frac-sub log1p-expm1-u div-inv
3×cube-div cube-mult pow-to-exp unpow-prod-down diff-log unpow3 cube-prod pow-prod-down prod-exp sum-log cos-mult cbrt-unprod sqr-pow
2×flip3-+ frac-add flip-+ distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- associate--l+ flip--
Counts
4 → 156
Calls
4 calls:
3.0ms
(pow (* (cos x) (cos eps)) 3)
3.0ms
(pow (* (cos x) (cos eps)) 3)
3.0ms
(pow (* (cos x) (cos eps)) 3)
11.4s
(- (+ (/ (/ (sin eps) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (cos eps)) (+ (* (/ (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)))) (fma (/ (pow (sin x) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (/ (pow (sin eps) 3) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))))) (/ (sin x) (cos x)))

series1.7s

Counts
4 → 12
Calls
4 calls:
72.0ms
(pow (* (cos x) (cos eps)) 3)
64.0ms
(pow (* (cos x) (cos eps)) 3)
59.0ms
(pow (* (cos x) (cos eps)) 3)
1.5s
(- (+ (/ (/ (sin eps) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (cos eps)) (+ (* (/ (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)))) (fma (/ (pow (sin x) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (/ (pow (sin eps) 3) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))))) (/ (sin x) (cos x)))

simplify1.6s

Counts
168 → 168
Iterations

Useful iterations: 2 (389.0ms)

IterNodesCost
032522331
194320979
2425918142
done500018142

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

regimes221.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
040164
149164
done49164

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.4s3267×body1280valid
1.1s649×body2560valid
758.0ms1830×body640valid
214.0ms786×body320valid
93.0ms1065×body80valid
85.0ms403×body160valid