Details

Time bar (total: 2.3m)

sample384.0ms

Algorithm
intervals
Results
217.0ms107×body1280valid
74.0ms61×body640valid
53.0ms19×body2560valid
14.0ms17×body320valid
10.0ms43×body80valid
5.0ms9×body160valid

simplify60.0ms

Calls
1 calls:
Slowest
60.0ms
(- (tan (+ x eps)) (tan x))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize19.0ms

Local error

Found 2 expressions with local error:

3.2b
(tan (+ x eps))
1.0b
(- (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
12.0ms
(- (tan (+ x eps)) (tan x))
5.0ms
(tan (+ x eps))

series207.0ms

Calls
2 calls:
Slowest
111.0ms
(- (tan (+ x eps)) (tan x))
95.0ms
(tan (+ x eps))

simplify1.4s

Calls
15 calls:
Slowest
452.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
432.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
144.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
129.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
57.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune322.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize45.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (/ (+ (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))))

rewrite152.0ms

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
99.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
23.0ms
(* (tan x) (tan eps))
23.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms
(+ (tan x) (tan eps))

series1.1s

Calls
4 calls:
Slowest
524.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
312.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
141.0ms
(+ (tan x) (tan eps))
121.0ms
(* (tan x) (tan eps))

simplify5.7s

Calls
74 calls:
Slowest
471.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
470.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
439.0ms
(/ (* (* (+ (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)))))
367.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
361.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.1b

localize41.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (* (/ (+ (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))

rewrite184.0ms

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
98.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
56.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
14.0ms
(* (tan x) (tan eps))
13.0ms
(* (tan x) (tan eps))

series1.8s

Calls
4 calls:
Slowest
1.3s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
176.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
143.0ms
(* (tan x) (tan eps))
124.0ms
(* (tan x) (tan eps))

simplify11.3s

Calls
111 calls:
Slowest
845.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
820.0ms
(- (+ (/ (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)))
790.0ms
(- (+ (/ (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)))
735.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
591.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (/ (/ (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 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))))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
394×add-cbrt-cube add-exp-log
195×prod-exp cbrt-unprod
121×pow1
120×cbrt-undiv div-exp
51×frac-times pow-prod-down
33×associate-*l/ associate-*r/
25×add-sqr-sqrt
12×pow-sqr pow-prod-up
11×times-frac
10×*-un-lft-identity
6×pow-plus add-log-exp difference-of-squares
4×add-cube-cbrt insert-posit16
3×pow2 swap-sqr associate-*r* associate-*l* *-commutative
2×distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip--
Calls
4 calls:
Slowest
96.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
85.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
85.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
74.0ms
(- (/ (/ (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)))

series817.0ms

Calls
4 calls:
Slowest
304.0ms
(- (/ (/ (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)))
183.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
175.0ms
(* (* (/ (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))))

simplify1.6m

Calls
330 calls:
Slowest
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)))))
1.1s
(* (* (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (sin x) (cos x)) (/ (sin 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)))))
1.0s
(* (* (/ (* (* (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)))))
970.0ms
(* (* (/ (* (* (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)))))
940.0ms
(* (* (/ (* (* (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) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes138.0ms

Accuracy

0% (0.3b remaining)

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

bsearch12.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
4.6s3281×body1280valid
2.1s660×body2560valid
1.9s1879×body640valid
458.0ms726×body320valid
222.0ms1095×body80valid
144.0ms359×body160valid