Details

Time bar (total: 1.2m)

sample443.0ms

Algorithm
intervals
Results
256.0ms101×body1280valid
77.0ms67×body640valid
60.0ms16×body2560valid
23.0ms28×body320valid
9.0ms34×body80valid
6.0ms10×body160valid

simplify9.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
9.0ms
(- (tan (+ x eps)) (tan x))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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))

series220.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
133.0ms
(- (tan (+ x eps)) (tan x))
87.0ms
(tan (+ x eps))

simplify1.4s

Counts
15 → 33
Calls
15 calls:
Slowest
489.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
418.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
151.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
146.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
44.0ms
(- (* (sin (+ x eps)) (cos x)) (* (cos (+ x eps)) (sin x)))

prune371.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ (+ (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))))

rewrite136.0ms

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))
40.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms
(* (tan x) (tan eps))
14.0ms
(+ (tan x) (tan eps))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
570.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
306.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
161.0ms
(* (tan x) (tan eps))
124.0ms
(+ (tan x) (tan eps))

simplify5.5s

Counts
74 → 102
Calls
74 calls:
Slowest
557.0ms
(/ (* (* (+ (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
(+ x (+ (* 1/3 (pow x 3)) eps))
426.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
378.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
301.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.0b

localize47.0ms

Local error

Found 4 expressions with local error:

5.1b
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
0.2b
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
0.2b
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
104×*-un-lft-identity
83×add-sqr-sqrt
67×add-cube-cbrt
23×associate-/r*
19×add-exp-log
16×associate-/r/ distribute-lft-out
15×tan-quot
13×add-cbrt-cube
8×div-exp
7×pow1 div-inv
6×associate-/l* add-log-exp
5×flip3-+ frac-add flip-+ difference-of-squares
4×cbrt-undiv insert-posit16
3×associate-*r* associate-*l*
2×rec-exp clear-num frac-2neg flip3-- 1-exp flip-- distribute-lft-out-- associate-/l/
1×frac-times sub-neg diff-log div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod pow-flip inv-pow unswap-sqr
Counts
4 → 182
Calls
4 calls:
Slowest
138.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
36.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
18.0ms
(* (tan x) (tan eps))
18.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
508.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
454.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
338.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
111.0ms
(* (tan x) (tan eps))

simplify23.3s

Counts
222 → 194
Calls
222 calls:
Slowest
1.1s
(/ (* (* 1 1) 1) (* (* (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))) (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))))
443.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
384.0ms
(- (+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 1/3 eps))))
367.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
366.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps))))) (* (cbrt (+ (tan x) (tan eps))) (cbrt (+ (tan x) (tan eps))))))

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.0b

localize48.0ms

Local error

Found 4 expressions with local error:

7.5b
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.2b
(/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×tan-quot
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
12×frac-sub
10×*-un-lft-identity add-cube-cbrt
9×flip3-- flip--
8×pow1 associate-/l/
6×associate-*r* associate-*l* add-log-exp
4×flip3-+ frac-add flip-+ insert-posit16
3×times-frac prod-exp cbrt-unprod associate-/l*
2×frac-times cbrt-undiv div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub div-inv
Counts
4 → 96
Calls
4 calls:
Slowest
58.0ms
(/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
39.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
25.0ms
(* (tan x) (tan eps))
14.0ms
(* (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
477.0ms
(/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
320.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
136.0ms
(* (tan x) (tan eps))
117.0ms
(* (tan x) (tan eps))

simplify16.2s

Counts
77 → 108
Calls
77 calls:
Slowest
582.0ms
(/ (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (cos x)))
569.0ms
(* (- (tan x) (tan eps)) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))))
558.0ms
(* (* (cos x) (cos eps)) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))))
557.0ms
(/ (* (* (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))) (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))) (* (* (* (- 1 (* (tan x) (tan eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x))))
508.0ms
(+ (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps))) (/ (* (cos x) (sin eps)) (cos eps)))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes136.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch6.0ms

end0.0ms

sample13.1s

Algorithm
intervals
Results
6.9s3351×body1280valid
2.8s1821×body640valid
2.1s600×body2560valid
793.0ms743×body320valid
237.0ms1147×body80valid
183.0ms338×body160valid