Details

Time bar (total: 46.9s)

sample443.0ms

Algorithm
intervals
Results
252.0ms109×body1280valid
79.0ms25×body2560valid
68.0ms55×body640valid
15.0ms20×body320valid
10.0ms39×body80valid
4.0ms8×body160valid

simplify17.0ms

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

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize16.0ms

Local error

Found 2 expressions with local error:

1.8b
(- (tan (+ x eps)) (tan x))
1.7b
(tan (+ x eps))

rewrite8.0ms

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
6.0ms
(- (tan (+ x eps)) (tan x))
2.0ms
(tan (+ x eps))

series200.0ms

Calls
2 calls:
Slowest
132.0ms
(- (tan (+ x eps)) (tan x))
68.0ms
(tan (+ x eps))

simplify879.0ms

Calls
15 calls:
Slowest
405.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
129.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
90.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
69.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
37.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune398.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.3b

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (/ (+ (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))))

rewrite90.0ms

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
39.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
28.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
12.0ms
(+ (tan x) (tan eps))
10.0ms
(* (tan x) (tan eps))

series860.0ms

Calls
4 calls:
Slowest
423.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
243.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
106.0ms
(* (tan x) (tan eps))
88.0ms
(+ (tan x) (tan eps))

simplify4.6s

Calls
72 calls:
Slowest
624.0ms
(/ (* (* (+ (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)))))
475.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
308.0ms
(- (+ (/ (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)))
253.0ms
(- (+ (/ (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)))
249.0ms
(/ (+ (/ (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: 16.1b

localize39.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
0.2b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(* (sin x) (sin eps))
0.1b
(+ (tan x) (tan eps))

rewrite102.0ms

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
77.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
16.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
4.0ms
(* (sin x) (sin eps))
4.0ms
(+ (tan x) (tan eps))

series701.0ms

Calls
4 calls:
Slowest
423.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
114.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
113.0ms
(+ (tan x) (tan eps))
50.0ms
(* (sin x) (sin eps))

simplify6.4s

Calls
46 calls:
Slowest
573.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
549.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
528.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
513.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
324.0ms
(- (+ (/ (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)))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.1b

localize31.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (+ (/ (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)))
0.2b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(* (sin x) (sin eps))

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
11×add-sqr-sqrt *-un-lft-identity
9×prod-exp cbrt-unprod add-log-exp
8×cbrt-undiv div-exp
6×pow1 add-cube-cbrt
4×insert-posit16
3×times-frac associate-*r* associate-*l* frac-sub sin-mult
2×clear-num associate-/r* frac-2neg diff-log associate-/r/ cos-mult div-inv associate-/l* distribute-lft-out-- difference-of-squares associate-/l/
1×sum-log sub-neg flip3-+ flip3-- pow-prod-down frac-add associate--l+ *-commutative flip-+ flip-- distribute-lft-out
Calls
4 calls:
Slowest
203.0ms
(- (+ (/ (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)))
9.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
9.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
4.0ms
(* (sin x) (sin eps))

series707.0ms

Calls
4 calls:
Slowest
441.0ms
(- (+ (/ (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)))
113.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
97.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
56.0ms
(* (sin x) (sin eps))

simplify13.3s

Calls
62 calls:
Slowest
718.0ms
(- (* (- (* (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (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) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))))) (cos x)) (* (- (/ (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)))
662.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
646.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
621.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
599.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.1b

regimes114.0ms

Accuracy

0% (0.4b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch4.0ms

end0.0ms

sample13.2s

Algorithm
intervals
Results
6.7s3273×body1280valid
2.8s1825×body640valid
2.5s715×body2560valid
616.0ms755×body320valid
257.0ms1079×body80valid
163.0ms353×body160valid