Details

Time bar (total: 27.5s)

sample313.0ms

Algorithm
intervals
Results
185.0ms106×body1280valid
54.0ms19×body2560valid
40.0ms57×body640valid
14.0ms30×body320valid
6.0ms36×body80valid
2.0ms8×body160valid

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize14.0ms

Local error

Found 2 expressions with local error:

1.0b
(- (tan (+ x eps)) (tan x))
3.0b
(tan (+ x eps))

rewrite37.0ms

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:
29.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series210.0ms

Counts
2 → 6
Calls
2 calls:
117.0ms
(- (tan (+ x eps)) (tan x))
93.0ms
(tan (+ x eps))

simplify1.7s

Counts
33 → 33
Iterations
IterNodes
done5001
41821
3719
2300
1139
070

prune214.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b
(* (tan x) (tan eps))
2.8b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite227.0ms

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:
16.0ms
(+ (tan x) (tan eps))
55.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
30.0ms
(* (tan x) (tan eps))
123.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
126.0ms
(+ (tan x) (tan eps))
298.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
130.0ms
(* (tan x) (tan eps))
557.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.6s

Counts
102 → 102
Iterations
IterNodes
done5000
34143
21152
1405
0174

prune610.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (tan x))
0.6b
(cbrt (tan x))
0.6b
(cbrt (tan x))
2.8b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×cbrt-prod *-un-lft-identity
7×add-cube-cbrt
6×add-log-exp
4×pow1 add-cbrt-cube tan-quot add-exp-log insert-posit16
3×cbrt-div pow1/3
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log frac-sub flip-- distribute-lft-out--
Counts
4 → 56
Calls
4 calls:
2.0ms
(cbrt (tan x))
2.0ms
(cbrt (tan x))
2.0ms
(cbrt (tan x))
115.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))

series916.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(cbrt (tan x))
150.0ms
(cbrt (tan x))
149.0ms
(cbrt (tan x))
471.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))

simplify1.7s

Counts
68 → 68
Iterations
IterNodes
done5001
31487
2496
1214
098

prune541.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (cos x))
0.2b
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.2b
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
2.8b
(+ (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (- (/ (/ (sin eps) (cos eps)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x))))

rewrite432.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
56×times-frac
51×*-un-lft-identity
40×add-cube-cbrt
30×add-cbrt-cube add-exp-log
26×associate-*r* associate-*l*
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod unswap-sqr
5×div-inv
4×insert-posit16
3×associate-/r* frac-add distribute-lft-out associate-/l*
2×frac-times associate-+r+ sum-log pow-prod-down associate-*l/ associate-*r/ *-commutative distribute-lft-out--
1×+-commutative quot-tan clear-num associate-+r- sub-neg frac-2neg flip3-+ flip3-- diff-log frac-sub flip-+ flip--
Counts
4 → 153
Calls
4 calls:
10.0ms
(/ (sin x) (cos x))
42.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
35.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
340.0ms
(+ (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (- (/ (/ (sin eps) (cos eps)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x))))

series873.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (sin x) (cos x))
144.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
159.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
544.0ms
(+ (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (- (/ (/ (sin eps) (cos eps)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x))))

simplify3.2s

Counts
165 → 165
Iterations
IterNodes
done5006
22529
1637
0219

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

regimes189.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done18
118
016

end0.0ms

sample11.2s

Algorithm
intervals
Results
5.9s3282×body1280valid
2.2s1804×body640valid
2.0s658×body2560valid
596.0ms767×body320valid
197.0ms1136×body80valid
123.0ms353×body160valid