Details

Time bar (total: 56.9s)

sample475.0ms

Algorithm
intervals
Results
195.0ms89×body1280valid
98.0ms72×body640valid
92.0ms29×body2560valid
62.0ms22×body320valid
9.0ms37×body80valid
4.0ms7×body160valid

simplify17.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize27.0ms

Local error

Found 2 expressions with local error:

3.6b
(tan (+ x eps))
1.0b
(- (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))
10.0ms
(tan (+ x eps))

series229.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
130.0ms
(- (tan (+ x eps)) (tan x))
99.0ms
(tan (+ x eps))

simplify1.3s

Counts
15 → 33
Calls
15 calls:
Slowest
416.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
414.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
144.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
137.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
38.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune372.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.3b

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.3b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite161.0ms

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
73.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
46.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
26.0ms
(* (tan x) (tan eps))
14.0ms
(+ (tan x) (tan eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
512.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
290.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
133.0ms
(+ (tan x) (tan eps))
115.0ms
(* (tan x) (tan eps))

simplify5.6s

Counts
74 → 102
Calls
74 calls:
Slowest
493.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
456.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
441.0ms
(/ (* (* (+ (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)))))
394.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
334.0ms
(- (+ (/ (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)))

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.2b

localize67.0ms

Local error

Found 4 expressions with local error:

9.4b
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
0.3b
(* (tan x) (tan eps))
0.3b
(* (tan x) (tan eps))
0.2b
(* (+ (tan x) (tan eps)) (cos x))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
17×associate-*l/
16×add-sqr-sqrt
14×tan-quot
12×*-un-lft-identity
10×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
9×associate-*r*
6×frac-sub add-log-exp
4×flip3-- insert-posit16 flip--
3×flip3-+ pow-prod-down frac-add prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
2×frac-times associate-*r/
1×sub-neg diff-log distribute-lft-out
Counts
4 → 86
Calls
4 calls:
Slowest
35.0ms
(* (+ (tan x) (tan eps)) (cos x))
34.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
16.0ms
(* (tan x) (tan eps))
14.0ms
(* (tan x) (tan eps))

series737.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
197.0ms
(* (+ (tan x) (tan eps)) (cos x))
136.0ms
(* (tan x) (tan eps))
135.0ms
(* (tan x) (tan eps))

simplify8.3s

Counts
66 → 98
Calls
66 calls:
Slowest
525.0ms
(+ (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps))) (/ (* (cos x) (sin eps)) (cos eps)))
511.0ms
(- (* (* (+ (pow (tan x) 3) (pow (tan eps) 3)) (cos x)) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (* (+ (* (tan x) (tan x)) (- (* (tan eps) (tan eps)) (* (tan x) (tan eps)))) (* (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (sin x))))
493.0ms
(* (- (tan x) (tan eps)) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))))
461.0ms
(+ (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps))) (/ (* (cos x) (sin eps)) (cos eps)))
450.0ms
(* (* (cos x) (cos eps)) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan eps))
0.2b
(/ (sin x) (/ (cos x) (sin x)))
0.2b
(* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x)))
0.2b
(/ (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
86×times-frac
63×add-sqr-sqrt
58×*-un-lft-identity
56×add-cube-cbrt
37×add-cbrt-cube add-exp-log
16×associate-*l*
14×associate-/r*
12×cbrt-undiv div-exp
10×prod-exp cbrt-unprod
8×pow1
7×associate-*r* div-inv
5×frac-times associate-*l/ associate-*r/ associate-/l/
4×flip3-+ tan-quot flip-+ insert-posit16 associate-/l* add-log-exp
3×associate-/r/ unswap-sqr
2×clear-num frac-2neg pow-prod-down *-commutative
1×distribute-rgt-in distribute-lft-in flip3-- flip-- distribute-lft-out
Counts
4 → 166
Calls
4 calls:
Slowest
73.0ms
(* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x)))
53.0ms
(/ (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
23.0ms
(* (tan x) (tan eps))
17.0ms
(/ (sin x) (/ (cos x) (sin x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
791.0ms
(/ (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
197.0ms
(* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x)))
125.0ms
(* (tan x) (tan eps))
53.0ms
(/ (sin x) (/ (cos x) (sin x)))

simplify15.1s

Counts
181 → 178
Calls
181 calls:
Slowest
1.9s
(/ (* (* (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x))) (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x)))) (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x)))) (* (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos x)) (cos x))))
547.0ms
(* (/ (* (* (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 x))) (cos x))) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x))))
505.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (/ (* (* (cos x) (cos x)) (cos x)) (* (* (sin x) (sin x)) (sin x))))
421.0ms
(+ (* (/ (sin x) (/ (cos x) (sin x))) (/ (sin x) (/ (cos x) (sin x)))) (- (* (cos x) (cos x)) (* (/ (sin x) (/ (cos x) (sin x))) (cos x))))
415.0ms
(- (+ (- (log (sin eps)) (log (cos eps))) (log (+ (/ (sin x) (/ (cos x) (sin x))) (cos x)))) (+ (log (- 1 (* (tan x) (tan eps)))) (log (cos x))))

prune3.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes250.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch6.0ms

end0.0ms

sample15.9s

Algorithm
intervals
Results
8.7s3279×body1280valid
2.7s1784×body640valid
2.5s658×body2560valid
1.1s783×body320valid
361.0ms1126×body80valid
253.0ms370×body160valid