Details

Time bar (total: 28.4s)

sample344.0ms

Algorithm
intervals
Results
170.0ms101×body1280valid
86.0ms29×body2560valid
46.0ms61×body640valid
12.0ms24×body320valid
5.0ms33×body80valid
2.0ms8×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize16.0ms

Local error

Found 2 expressions with local error:

1.0b
(- (tan (+ x eps)) (tan x))
2.3b
(tan (+ x eps))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity tan-quot add-log-exp
2×pow1 tan-sum add-cbrt-cube add-exp-log frac-sub add-cube-cbrt
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 25
Calls
2 calls:
13.0ms
(- (tan (+ x eps)) (tan x))
5.0ms
(tan (+ x eps))

series233.0ms

Counts
2 → 6
Calls
2 calls:
122.0ms
(- (tan (+ x eps)) (tan x))
112.0ms
(tan (+ x eps))

simplify734.0ms

Counts
31 → 31
Iterations

Useful iterations: done (732.0ms)

IterNodesCost
068367
1137355
2355341
31176337
done5000335

prune192.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.7b

localize28.0ms

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))
2.2b
(- (/ (+ (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-cbrt-cube add-exp-log add-log-exp
6×pow1
5×distribute-lft-out
4×associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×flip3-+ flip3-- frac-add associate-/r/ flip-+ flip-- difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 86
Calls
4 calls:
40.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
6.0ms
(+ (tan x) (tan eps))
11.0ms
(* (tan x) (tan eps))
78.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
312.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
151.0ms
(+ (tan x) (tan eps))
130.0ms
(* (tan x) (tan eps))
565.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify814.0ms

Counts
98 → 98
Iterations

Useful iterations: done (810.0ms)

IterNodesCost
01701724
14111649
216631579
done50001578

prune701.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.6b

localize59.0ms

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)
2.2b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
45×tan-quot
21×frac-times add-cbrt-cube add-exp-log
19×pow-prod-down
15×associate-*r/
14×associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×add-log-exp
5×frac-sub
4×associate-*r* associate-*l* pow-sqr pow-prod-up
3×cube-div pow-unpow
2×pow-pow flip3-+ pow-plus pow-exp associate--l+ *-commutative flip-+ rem-cube-cbrt
1×pow2 distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down distribute-lft-in flip3-- diff-log unpow3 cube-prod swap-sqr flip-- unswap-sqr sqr-pow
Counts
4 → 114
Calls
4 calls:
22.0ms
(* (tan x) (tan eps))
78.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
18.0ms
(pow (* (tan x) (tan eps)) 3)
75.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series2.8s

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (tan x) (tan eps))
148.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
181.0ms
(pow (* (tan x) (tan eps)) 3)
2.3s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify455.0ms

Counts
126 → 126
Iterations

Useful iterations: done (449.0ms)

IterNodesCost
02553217
19092506
done50012298

prune697.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize182.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (* (cos eps) (cos x)) 3)
0.6b
(pow (* (cos eps) (cos x)) 3)
0.6b
(pow (* (cos eps) (cos x)) 3)
2.3b
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (* (pow (cos x) 2) (pow (cos eps) 3)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))))) (/ (sin eps) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))) (cos eps)))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))))) (/ (sin x) (cos x)))

rewrite8.4s

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
13×pow1 add-cbrt-cube add-exp-log add-log-exp
12×add-sqr-sqrt
9×pow-unpow
7×add-cube-cbrt
6×pow-pow pow-exp rem-cube-cbrt
5×frac-sub
4×frac-add
3×cube-div cube-mult pow-to-exp sum-log unpow-prod-down diff-log unpow3 cube-prod pow-prod-down prod-exp cos-mult cbrt-unprod distribute-lft-out distribute-lft-out-- sqr-pow
2×flip3-+ flip-+ difference-of-squares
1×sub-neg times-frac flip3-- associate--l+ flip--
Counts
4 → 94
Calls
4 calls:
6.0ms
(pow (* (cos eps) (cos x)) 3)
8.0ms
(pow (* (cos eps) (cos x)) 3)
6.0ms
(pow (* (cos eps) (cos x)) 3)
8.3s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (* (pow (cos x) 2) (pow (cos eps) 3)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))))) (/ (sin eps) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))) (cos eps)))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))))) (/ (sin x) (cos x)))

series1.4s

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (* (cos eps) (cos x)) 3)
67.0ms
(pow (* (cos eps) (cos x)) 3)
68.0ms
(pow (* (cos eps) (cos x)) 3)
1.2s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (* (pow (cos x) 2) (pow (cos eps) 3)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))))) (/ (sin eps) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))) (cos eps)))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos eps) (cos x)) 3))))) (/ (sin x) (cos x)))

simplify1.0s

Counts
106 → 106
Iterations

Useful iterations: 2 (314.0ms)

IterNodesCost
01855777
16005507
238075273
done50015273

prune964.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes260.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
045171
163169
264169
done64169

end0.0ms

sample7.6s

Algorithm
intervals
Results
3.9s3232×body1280valid
1.3s633×body2560valid
1.2s1874×body640valid
583.0ms759×body320valid
229.0ms1135×body80valid
79.0ms367×body160valid