Details

Time bar (total: 27.2s)

sample380.0ms

Algorithm
intervals
Results
144.0ms85×body1280valid
70.0ms20×body2560valid
67.0ms63×body640valid
54.0ms46×body80valid
20.0ms29×body320valid
13.0ms13×body160valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize22.0ms

Local error

Found 2 expressions with local error:

1.0b
(- (tan (+ x eps)) (tan x))
4.3b
(tan (+ x eps))

rewrite49.0ms

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:
40.0ms
(- (tan (+ x eps)) (tan x))
9.0ms
(tan (+ x eps))

series208.0ms

Counts
2 → 6
Calls
2 calls:
138.0ms
(- (tan (+ x eps)) (tan x))
69.0ms
(tan (+ x eps))

simplify1.3s

Counts
33 → 33
Iterations
IterNodes
done2017
52017
41821
3719
2300
1139
070

prune329.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize30.0ms

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))
3.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite154.0ms

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:
47.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms
(+ (tan x) (tan eps))
15.0ms
(* (tan x) (tan eps))
82.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
343.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
141.0ms
(+ (tan x) (tan eps))
145.0ms
(* (tan x) (tan eps))
518.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts
102 → 102
Iterations
IterNodes
done2000
32000
21148
1405
0174

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
3.4b
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×tan-quot
19×*-un-lft-identity
18×associate-*r*
15×add-exp-log
14×add-cube-cbrt
11×times-frac add-cbrt-cube
8×pow1 frac-sub add-log-exp
7×frac-times associate-*l* associate-*l/
5×flip3-+ frac-add prod-exp flip-+
4×insert-posit16 unswap-sqr
3×associate-*r/ cbrt-unprod
2×flip3-- div-exp pow-prod-down associate-/r/ un-div-inv *-commutative flip-- distribute-lft-out
1×cbrt-undiv +-commutative rec-exp sum-log sub-neg diff-log 1-exp div-inv
Counts
4 → 103
Calls
4 calls:
47.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
15.0ms
(+ (tan x) (tan eps))
37.0ms
(* (tan x) (tan eps))
49.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
346.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
136.0ms
(+ (tan x) (tan eps))
138.0ms
(* (tan x) (tan eps))
554.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify1.3s

Counts
115 → 115
Iterations
IterNodes
done2002
32002
21782
1571
0227

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
3.4b
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×tan-quot
19×*-un-lft-identity
18×associate-*r*
15×add-exp-log
14×add-cube-cbrt
11×times-frac add-cbrt-cube
8×pow1 frac-sub add-log-exp
7×frac-times associate-*l* associate-*l/
5×flip3-+ frac-add prod-exp flip-+
4×insert-posit16 unswap-sqr
3×associate-*r/ cbrt-unprod
2×flip3-- div-exp pow-prod-down associate-/r/ un-div-inv *-commutative flip-- distribute-lft-out
1×cbrt-undiv +-commutative rec-exp sum-log sub-neg diff-log 1-exp div-inv
Counts
4 → 103
Calls
4 calls:
34.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
10.0ms
(+ (tan x) (tan eps))
14.0ms
(* (tan x) (tan eps))
27.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series973.0ms

Counts
4 → 12
Calls
4 calls:
285.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
115.0ms
(+ (tan x) (tan eps))
137.0ms
(* (tan x) (tan eps))
436.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify1.3s

Counts
115 → 115
Iterations
IterNodes
done2002
32002
21782
1571
0227

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.9b

regimes269.0ms

Accuracy

90.8% (0.7b remaining)

Error of 15.2b against oracle of 14.5b and baseline of 21.9b

bsearch247.0ms

Steps
ItersRangePoint
8
1.9244747225358218e-24
2.6911921325060526e-20
2.7293458866662548e-21
6
-2.134234128465575e-22
-4.566239321798029e-23
-2.1070254757403724e-22

simplify6.0ms

Iterations
IterNodes
done40
140
028

end0.0ms

sample13.3s

Algorithm
intervals
Results
6.1s3322×body1280valid
2.7s633×body2560valid
2.5s1785×body640valid
1.1s823×body320valid
344.0ms1114×body80valid
212.0ms323×body160valid