Details

Time bar (total: 47.9s)

sample378.0ms

Algorithm
intervals
Results
209.0ms108×body1280valid
65.0ms48×body640valid
58.0ms19×body2560valid
18.0ms25×body320valid
9.0ms41×body80valid
6.0ms15×body160valid

simplify10.0ms

Calls
1 calls:
Slowest
10.0ms
(- (tan (+ x eps)) (tan x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize14.0ms

Local error

Found 2 expressions with local error:

3.0b
(tan (+ x eps))
1.6b
(- (tan (+ x eps)) (tan x))

rewrite14.0ms

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
Calls
2 calls:
Slowest
11.0ms
(- (tan (+ x eps)) (tan x))
2.0ms
(tan (+ x eps))

series167.0ms

Calls
2 calls:
Slowest
97.0ms
(- (tan (+ x eps)) (tan x))
70.0ms
(tan (+ x eps))

simplify1.3s

Calls
15 calls:
Slowest
489.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
412.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
119.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
58.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
37.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune341.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize17.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (/ (+ (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))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
20×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--
Calls
4 calls:
Slowest
61.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
29.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
10.0ms
(* (tan x) (tan eps))
8.0ms
(+ (tan x) (tan eps))

series950.0ms

Calls
4 calls:
Slowest
462.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
276.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
109.0ms
(+ (tan x) (tan eps))
102.0ms
(* (tan x) (tan eps))

simplify4.5s

Calls
72 calls:
Slowest
492.0ms
(/ (* (* (+ (tan x) (tan eps)) (+ (tan x) (tan eps))) (+ (tan x) (tan eps))) (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))))
412.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
306.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
299.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
246.0ms
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.5b

localize20.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (* (/ (+ (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)))
0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
45×tan-quot
35×pow1
21×frac-times
20×add-cbrt-cube add-exp-log
15×pow-prod-down associate-*r/
14×associate-*l/
10×prod-exp cbrt-unprod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
6×add-log-exp
5×frac-sub
4×pow-prod-up insert-posit16
3×*-commutative
2×flip3-+ pow-plus associate--l+ flip-+
1×pow2 distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log flip--
Calls
4 calls:
Slowest
47.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
17.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
6.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))

series1.4s

Calls
4 calls:
Slowest
1.1s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
113.0ms
(* (tan x) (tan eps))
104.0ms
(* (tan x) (tan eps))
93.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))

simplify8.8s

Calls
97 calls:
Slowest
752.0ms
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (/ (sin eps) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))))) (/ (sin x) (cos x)))
732.0ms
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (/ (sin eps) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))))) (/ (sin x) (cos x)))
530.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
370.0ms
(- (* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x)) (* (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (sin x)))
362.0ms
(- (* (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

localize34.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
0.3b
(* (cos eps) (cos eps))
0.2b
(* (* (tan x) (sin eps)) (* (tan x) (sin eps)))
0.2b
(* (tan x) (tan eps))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
38×pow1
20×add-cbrt-cube add-exp-log
15×pow-prod-down
13×tan-quot
10×prod-exp cbrt-unprod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l* associate-*l/
6×add-log-exp
5×pow-prod-up frac-sub
4×frac-times associate-*r/ insert-posit16
3×pow-plus *-commutative
2×pow2 flip3-+ associate--l+ flip-+
1×distribute-rgt-in sqr-cos sub-neg distribute-lft-in flip3-- diff-log cos-mult flip--
Calls
4 calls:
Slowest
22.0ms
(* (* (tan x) (sin eps)) (* (tan x) (sin eps)))
20.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
10.0ms
(* (tan x) (tan eps))
4.0ms
(* (cos eps) (cos eps))

series1.3s

Calls
4 calls:
Slowest
1.0s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
111.0ms
(* (tan x) (tan eps))
92.0ms
(* (* (tan x) (sin eps)) (* (tan x) (sin eps)))
17.0ms
(* (cos eps) (cos eps))

simplify8.8s

Calls
78 calls:
Slowest
778.0ms
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (/ (sin eps) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))))) (/ (sin x) (cos x)))
708.0ms
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (/ (sin eps) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))))) (/ (sin x) (cos x)))
587.0ms
(* (* (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps)))) (- 1 (* (tan x) (tan eps)))) (cos x))
505.0ms
(- (* (* (+ (tan x) (tan eps)) (+ (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (cos x)) (* (* (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps)))) (+ (* 1 1) (- (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (sin x)))
498.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (sin eps) (sin eps)) (sin eps))))

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

regimes290.0ms

Accuracy

88.8% (0.8b remaining)

Error of 15.4b against oracle of 14.6b and baseline of 22.1b

bsearch443.0ms

end0.0ms

sample14.6s

Algorithm
intervals
Results
7.6s3322×body1280valid
3.1s1822×body640valid
2.2s636×body2560valid
1.0s815×body320valid
248.0ms1060×body80valid
245.0ms345×body160valid