Details

Time bar (total: 41.7s)

sample499.0ms

Algorithm
intervals
Results
229.0ms99×body1280valid
99.0ms28×body2560valid
77.0ms59×body640valid
64.0ms24×body320valid
9.0ms34×body80valid
7.0ms12×body160valid

simplify16.0ms

Calls
1 calls:
Slowest
15.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize27.0ms

Local error

Found 2 expressions with local error:

2.5b
(tan (+ x eps))
1.5b
(- (tan (+ x eps)) (tan x))

rewrite17.0ms

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
13.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series174.0ms

Calls
2 calls:
Slowest
94.0ms
(- (tan (+ x eps)) (tan x))
79.0ms
(tan (+ x eps))

simplify926.0ms

Calls
15 calls:
Slowest
348.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
157.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
130.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
53.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
48.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune323.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.9b

localize19.0ms

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))))

rewrite117.0ms

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
67.0ms
(- (/ (+ (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))
10.0ms
(* (tan x) (tan eps))

series862.0ms

Calls
4 calls:
Slowest
427.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
222.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
112.0ms
(* (tan x) (tan eps))
100.0ms
(+ (tan x) (tan eps))

simplify4.2s

Calls
72 calls:
Slowest
533.0ms
(/ (* (* (+ (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)))))
394.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
269.0ms
(- (+ (/ (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)))
251.0ms
(- (+ (/ (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)))
237.0ms
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.8b

localize36.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(* (sin x) (sin eps))
0.1b
(+ (tan x) (tan eps))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×*-un-lft-identity
8×add-log-exp
6×pow1 add-cube-cbrt
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp insert-posit16
3×associate-*r* associate-*l* tan-quot
2×times-frac sin-mult difference-of-squares
1×+-commutative clear-num associate-/r* sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log pow-prod-down frac-add associate-/r/ cos-mult *-commutative frac-sub flip-+ div-inv flip-- distribute-lft-out associate-/l* distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
62.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
19.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
9.0ms
(* (sin x) (sin eps))
8.0ms
(+ (tan x) (tan eps))

series707.0ms

Calls
4 calls:
Slowest
423.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
116.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
114.0ms
(+ (tan x) (tan eps))
54.0ms
(* (sin x) (sin eps))

simplify6.5s

Calls
46 calls:
Slowest
638.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
615.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
611.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
581.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
291.0ms
(- (+ (/ (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)))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.8b

localize29.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (/ (+ (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))

rewrite44.0ms

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
22.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
11.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))

series1.3s

Calls
4 calls:
Slowest
945.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
126.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
103.0ms
(* (tan x) (tan eps))
88.0ms
(* (tan x) (tan eps))

simplify8.6s

Calls
97 calls:
Slowest
774.0ms
(- (+ (/ (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)))
664.0ms
(- (+ (/ (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)))
517.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
393.0ms
(- (* (* (/ (+ (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)))
359.0ms
(- (* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x)) (* (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (sin x)))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.8b

regimes273.0ms

Accuracy

90.5% (0.7b remaining)

Error of 15.3b against oracle of 14.6b and baseline of 21.9b

bsearch336.0ms

end0.0ms

sample12.4s

Algorithm
intervals
Results
6.5s3243×body1280valid
2.6s1823×body640valid
2.0s658×body2560valid
721.0ms804×body320valid
210.0ms1110×body80valid
149.0ms362×body160valid