Details

Time bar (total: 1.5m)

sample444.0ms

Algorithm
intervals
Results
260.0ms111×body1280valid
75.0ms23×body2560valid
65.0ms58×body640valid
17.0ms21×body320valid
9.0ms35×body80valid
3.0ms8×body160valid

simplify17.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
17.0ms
(- (tan (+ x eps)) (tan x))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize26.0ms

Local error

Found 2 expressions with local error:

4.2b
(tan (+ x eps))
1.5b
(- (tan (+ x eps)) (tan x))

rewrite34.0ms

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
25.0ms
(- (tan (+ x eps)) (tan x))
9.0ms
(tan (+ x eps))

series533.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
441.0ms
(tan (+ x eps))
93.0ms
(- (tan (+ x eps)) (tan x))

simplify1.4s

Counts
15 → 33
Calls
15 calls:
Slowest
499.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
403.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
132.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
130.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
44.0ms
(- (* (sin (+ x eps)) (cos x)) (* (cos (+ x eps)) (sin x)))

prune386.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.8b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))

rewrite108.0ms

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
65.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
22.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
13.0ms
(* (tan x) (tan eps))
7.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
509.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
323.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
140.0ms
(* (tan x) (tan eps))
136.0ms
(+ (tan x) (tan eps))

simplify5.8s

Counts
74 → 102
Calls
74 calls:
Slowest
545.0ms
(/ (* (* (+ (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)))))
491.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
419.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
397.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
372.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.6b

localize40.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (* (/ (+ (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))

rewrite171.0ms

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--
Counts
4 → 114
Calls
4 calls:
Slowest
75.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
57.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
21.0ms
(* (tan x) (tan eps))
16.0ms
(* (tan x) (tan eps))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
157.0ms
(* (tan x) (tan eps))
148.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
131.0ms
(* (tan x) (tan eps))

simplify10.9s

Counts
111 → 126
Calls
111 calls:
Slowest
861.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
829.0ms
(- (+ (/ (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)))
819.0ms
(- (+ (/ (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)))
791.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
419.0ms
(- (* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x)) (* (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (sin x)))

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize156.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (/ (/ (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 eps) (cos eps)) (/ (sin eps) (cos eps)))
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))))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
158×add-cbrt-cube add-exp-log
105×add-sqr-sqrt
91×times-frac
73×prod-exp cbrt-unprod
66×*-un-lft-identity
60×add-cube-cbrt
57×pow1
48×cbrt-undiv div-exp
27×swap-sqr associate-*r* associate-*l*
19×frac-times pow-prod-down
13×associate-*l/ associate-*r/
8×div-inv unswap-sqr
6×pow-sqr pow-prod-up add-log-exp difference-of-squares
4×pow-plus insert-posit16
3×pow2 *-commutative
2×distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 250
Calls
4 calls:
Slowest
103.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
89.0ms
(- (/ (/ (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)))
25.0ms
(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
18.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
298.0ms
(- (/ (/ (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)))
151.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
61.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
58.0ms
(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))

simplify50.9s

Counts
284 → 262
Calls
284 calls:
Slowest
1.6s
(* (* (/ (* (* (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 eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (sin x) (cos x)) (/ (sin 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)))))
1.2s
(* (* (/ (* (* (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) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
950.0ms
(+ (+ (- (log (sin x)) (log (cos x))) (- (log (sin eps)) (log (cos eps)))) (+ (- (log (sin x)) (log (cos x))) (- (log (sin eps)) (log (cos eps)))))

prune2.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes174.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch5.0ms

end0.0ms

sample10.1s

Algorithm
intervals
Results
4.9s3360×body1280valid
2.0s1813×body640valid
1.6s646×body2560valid
784.0ms785×body320valid
415.0ms340×body160valid
205.0ms1056×body80valid