Details

Time bar (total: 2.0m)

sample420.0ms

Algorithm
intervals
Results
213.0ms97×body1280valid
71.0ms59×body640valid
70.0ms21×body2560valid
30.0ms42×body80valid
18.0ms24×body320valid
6.0ms13×body160valid

simplify10.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize28.0ms

Local error

Found 2 expressions with local error:

2.7b
(tan (+ x eps))
1.5b
(- (tan (+ x eps)) (tan x))

rewrite19.0ms

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
12.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series234.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
134.0ms
(- (tan (+ x eps)) (tan x))
100.0ms
(tan (+ x eps))

simplify2.5s

Counts
40 → 33
Calls
40 calls:
Slowest
504.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
446.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
339.0ms
(* (* (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x))) (- (tan (+ x eps)) (tan x)))
201.0ms
(- (pow (tan (+ x eps)) 3) (pow (tan x) 3))
169.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))

prune391.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.7b

localize43.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ (+ (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))

rewrite140.0ms

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
97.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
23.0ms
(/ (+ (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
494.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
307.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
165.0ms
(* (tan x) (tan eps))
143.0ms
(+ (tan x) (tan eps))

simplify10.6s

Counts
123 → 102
Calls
123 calls:
Slowest
826.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
640.0ms
(* (* (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)))
490.0ms
(/ (* (* (+ (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)))))
450.0ms
(+ (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (+ (* (tan x) (tan x)) (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))))
449.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.6b

localize43.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))

rewrite183.0ms

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
93.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
40.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
27.0ms
(* (tan x) (tan eps))
20.0ms
(* (tan x) (tan eps))

series1.7s

Counts
4 → 12
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))
153.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
129.0ms
(* (tan x) (tan eps))
126.0ms
(* (tan x) (tan eps))

simplify16.6s

Counts
143 → 126
Calls
143 calls:
Slowest
813.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
802.0ms
(* (* (- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x)) (- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))) (- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x)))
759.0ms
(- (+ (/ (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)))
708.0ms
(- (+ (/ (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)))
626.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.4b

localize128.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (/ (/ (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)))
0.2b
(* (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
173×add-sqr-sqrt
128×*-un-lft-identity
109×add-cube-cbrt
97×add-cbrt-cube associate-*l* add-exp-log
35×cbrt-undiv div-exp prod-exp cbrt-unprod
32×difference-of-squares
27×associate-*r*
26×swap-sqr
23×pow1
14×div-inv
11×unswap-sqr
7×frac-times associate-*r/
6×add-log-exp
5×pow-prod-down associate-*l/
4×insert-posit16
3×*-commutative
2×pow2 pow-plus flip3-- associate-/r/ pow-sqr pow-prod-up flip-- distribute-lft-out--
1×sub-neg diff-log frac-sub
Counts
4 → 281
Calls
4 calls:
Slowest
90.0ms
(* (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))
52.0ms
(- (/ (/ (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)))
37.0ms
(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
35.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series760.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
338.0ms
(* (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))
319.0ms
(- (/ (/ (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)))
53.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
50.0ms
(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))

simplify1.1m

Counts
339 → 293
Calls
339 calls:
Slowest
1.4s
(* (/ (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))))) (* (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps))) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
1.4s
(* (/ (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))))) (* (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))))
1.3s
(* (/ (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))))) (* (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))))
1.2s
(* (/ (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))))) (* (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps))) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
1.1s
(* (/ (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))))) (* (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))))

prune3.8s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.3b

regimes245.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch8.0ms

end0.0ms

sample11.0s

Algorithm
intervals
Results
5.6s3336×body1280valid
2.4s1860×body640valid
2.1s622×body2560valid
462.0ms782×body320valid
240.0ms1070×body80valid
124.0ms330×body160valid