Details

Time bar (total: 1.9m)

sample502.0ms

Algorithm
intervals
Results
217.0ms111×body1280valid
177.0ms29×body2560valid
64.0ms56×body640valid
18.0ms19×body320valid
7.0ms32×body80valid
6.0ms9×body160valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize23.0ms

Local error

Found 2 expressions with local error:

3.3b
(tan (+ x eps))
1.3b
(- (tan (+ x eps)) (tan x))

rewrite18.0ms

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))
5.0ms
(tan (+ x eps))

series229.0ms

Calls
2 calls:
Slowest
135.0ms
(- (tan (+ x eps)) (tan x))
93.0ms
(tan (+ x eps))

simplify1.4s

Calls
15 calls:
Slowest
421.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
404.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
161.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
144.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
59.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune329.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.2b

localize42.0ms

Local error

Found 4 expressions with local error:

3.3b
(- (/ (+ (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))))

rewrite150.0ms

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
Calls
4 calls:
Slowest
106.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
23.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
13.0ms
(* (tan x) (tan eps))
7.0ms
(+ (tan x) (tan eps))

series1.1s

Calls
4 calls:
Slowest
495.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
311.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
146.0ms
(* (tan x) (tan eps))
144.0ms
(+ (tan x) (tan eps))

simplify5.7s

Calls
74 calls:
Slowest
512.0ms
(/ (* (* (+ (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)))))
459.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
425.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
398.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
335.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.1b

localize45.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (* (/ (+ (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))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
45×tan-quot
21×frac-times
20×add-cbrt-cube add-exp-log
19×pow-prod-down
15×associate-*r/
14×associate-*l/
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
6×add-log-exp
5×frac-sub
4×pow-sqr pow-prod-up insert-posit16
3×*-commutative
2×flip3-+ pow-plus associate--l+ flip-+ unswap-sqr
1×pow2 distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log swap-sqr flip--
Calls
4 calls:
Slowest
97.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
52.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
16.0ms
(* (tan x) (tan eps))
13.0ms
(* (tan x) (tan eps))

series1.6s

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))
167.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
145.0ms
(* (tan x) (tan eps))
140.0ms
(* (tan x) (tan eps))

simplify11.5s

Calls
111 calls:
Slowest
928.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
907.0ms
(- (+ (/ (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)))
808.0ms
(- (+ (/ (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)))
767.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
501.0ms
(- (* (* (/ (+ (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)))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

localize97.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
276×add-cbrt-cube add-exp-log
134×prod-exp cbrt-unprod
89×pow1
84×cbrt-undiv div-exp
65×add-sqr-sqrt
51×times-frac
38×*-un-lft-identity
35×frac-times pow-prod-down
32×add-cube-cbrt
23×associate-*l/ associate-*r/
15×swap-sqr associate-*r* associate-*l*
9×pow-sqr pow-prod-up
6×add-log-exp difference-of-squares
5×pow-plus
4×insert-posit16 div-inv unswap-sqr
3×pow2 *-commutative
2×distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip--
Calls
4 calls:
Slowest
101.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
87.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
47.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))
21.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series694.0ms

Calls
4 calls:
Slowest
309.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))
163.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
155.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
66.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify1.3m

Calls
307 calls:
Slowest
1.4s
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))) (* (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))
1.3s
(+ (+ (- (log (sin x)) (log (cos x))) (- (log (sin eps)) (log (cos eps)))) (+ (- (log (sin x)) (log (cos x))) (- (log (sin eps)) (log (cos eps)))))
1.2s
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))) (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))))
1.2s
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))) (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))))
1.1s
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))) (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))

prune3.2s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 0.2b

regimes238.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch5.0ms

end0.0ms

sample9.9s

Algorithm
intervals
Results
4.9s3260×body1280valid
2.3s1801×body640valid
1.6s653×body2560valid
697.0ms766×body320valid
240.0ms1138×body80valid
162.0ms382×body160valid