Details

Time bar (total: 45.3s)

sample323.0ms

Algorithm
intervals
Results
165.0ms98×body1280valid
66.0ms24×body2560valid
47.0ms56×body640valid
12.0ms22×body320valid
8.0ms44×body80valid
4.0ms12×body160valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize72.0ms

Local error

Found 2 expressions with local error:

2.0b
(- (tan (+ x eps)) (tan x))
2.9b
(tan (+ x eps))

rewrite45.0ms

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:
30.0ms
(- (tan (+ x eps)) (tan x))
12.0ms
(tan (+ x eps))

series384.0ms

Counts
2 → 6
Calls
2 calls:
228.0ms
(- (tan (+ x eps)) (tan x))
156.0ms
(tan (+ x eps))

simplify3.6s

Counts
33 → 33
Iterations
IterNodes
done5002
41752
3715
2300
1139
070

prune499.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.6b

localize89.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
2.9b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite238.0ms

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:
46.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms
(+ (tan x) (tan eps))
33.0ms
(* (tan x) (tan eps))
139.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series2.2s

Counts
4 → 12
Calls
4 calls:
647.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
231.0ms
(+ (tan x) (tan eps))
214.0ms
(* (tan x) (tan eps))
1.1s
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify6.7s

Counts
102 → 102
Iterations
IterNodes
done5038
34129
21135
1405
0174

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.4b

localize126.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.2b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.9b
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite345.0ms

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:
20.0ms
(* (tan x) (tan eps))
36.0ms
(* (tan x) (tan eps))
187.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
92.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series4.4s

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (tan x) (tan eps))
217.0ms
(* (tan x) (tan eps))
352.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.6s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify4.5s

Counts
126 → 126
Iterations
IterNodes
done5111
22722
1662
0204

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.4b

localize198.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (sin eps))
0.3b
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.3b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
2.9b
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
35×pow-prod-down
30×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
8×add-sqr-sqrt pow-sqr pow-prod-up
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×associate-*r* associate-*l* tan-quot frac-sub sin-mult
4×frac-times pow-plus associate-*r/ cos-mult insert-posit16
3×associate-*l/ *-commutative
2×pow2 flip3-+ swap-sqr associate--l+ flip-+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log flip-- unswap-sqr
Counts
4 → 116
Calls
4 calls:
16.0ms
(* (sin x) (sin eps))
75.0ms
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
61.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
186.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series3.5s

Counts
4 → 12
Calls
4 calls:
89.0ms
(* (sin x) (sin eps))
135.0ms
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
118.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
3.1s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify4.7s

Counts
128 → 128
Iterations
IterNodes
done5000
22813
1651
0217

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

regimes445.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations
IterNodes
done40
140
029

end0.0ms

sample8.6s

Algorithm
intervals
Results
4.3s3269×body1280valid
1.7s649×body2560valid
1.3s1897×body640valid
675.0ms761×body320valid
167.0ms1083×body80valid
126.0ms341×body160valid