Details

Time bar (total: 3.5m)

sample444.0ms

Algorithm
intervals
Results
232.0ms103×body1280valid
81.0ms22×body2560valid
71.0ms52×body640valid
30.0ms31×body320valid
12.0ms41×body80valid
4.0ms7×body160valid

simplify10.0ms

Counts
1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize62.0ms

Local error

Found 2 expressions with local error:

4.5b
(tan (+ x eps))
0.9b
(- (tan (+ x eps)) (tan x))

rewrite38.0ms

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 insert-posit16
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 27
Calls
2 calls:
Slowest
27.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series209.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
127.0ms
(- (tan (+ x eps)) (tan x))
82.0ms
(tan (+ x eps))

simplify1.3s

Counts
33 → 33

prune344.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.0b

localize22.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite144.0ms

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×insert-posit16 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 → 90
Calls
4 calls:
Slowest
84.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
26.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms
(* (tan x) (tan eps))
10.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
513.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
302.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
138.0ms
(+ (tan x) (tan eps))
126.0ms
(* (tan x) (tan eps))

simplify1.2s

Counts
102 → 102

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.8b

localize46.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))

rewrite304.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
73×tan-quot
37×frac-times
35×pow-prod-down
30×add-cbrt-cube add-exp-log
25×associate-*r/
24×associate-*l/
17×prod-exp cbrt-unprod
8×add-sqr-sqrt pow-sqr pow-prod-up
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×associate-*r* associate-*l* frac-sub
4×pow-plus insert-posit16
3×*-commutative
2×pow2 flip3-+ swap-sqr associate--l+ flip-+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log flip-- unswap-sqr
Counts
4 → 142
Calls
4 calls:
Slowest
99.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
96.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
90.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
15.0ms
(* (tan x) (tan eps))

series2.6s

Counts
4 → 12
Calls
4 calls:
Slowest
2.1s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
174.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
153.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
141.0ms
(* (tan x) (tan eps))

simplify2.0s

Counts
154 → 154

prune2.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.8b

localize175.0ms

Local error

Found 4 expressions with local error:

9.0b
(- (* (* (cos x) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (+ 1 (* (* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (* (+ (- (* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) 1) (sin x)))
0.3b
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))
0.3b
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))
0.3b
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))

rewrite10.4s

Algorithm
rewrite-expression-head
Rules
44928×tan-quot
25639×frac-times
13977×associate-*l/
13975×associate-*r/
12960×frac-add
297×flip3-+ flip-+
25×pow1
22×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
12×swap-sqr associate-*r* associate-*l* distribute-rgt1-in
10×add-cbrt-cube add-exp-log frac-sub
6×add-log-exp
4×distribute-rgt-in distribute-lft-in insert-posit16
3×pow2 pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
2×associate--l+
1×sub-neg flip3-- diff-log flip--
Counts
4 → 7027
Calls
4 calls:
Slowest
8.7s
(- (* (* (cos x) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (+ 1 (* (* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (* (+ (- (* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) 1) (sin x)))
329.0ms
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))
329.0ms
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))
328.0ms
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))

series4.1s

Counts
4 → 12
Calls
4 calls:
Slowest
3.4s
(- (* (* (cos x) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (+ 1 (* (* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (* (+ (- (* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) 1) (sin x)))
239.0ms
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))
220.0ms
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))
216.0ms
(* (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))

simplify23.9s

Counts
7039 → 7039

prune2.5m

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 13.8b

regimes327.0ms

Accuracy

89.5% (0.8b remaining)

Error of 15.3b against oracle of 14.5b and baseline of 21.7b

bsearch262.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
4.6s3374×body1280valid
2.0s648×body2560valid
2.0s1779×body640valid
424.0ms749×body320valid
190.0ms1100×body80valid
139.0ms350×body160valid