Details

Time bar (total: 50.7s)

sample333.0ms

Algorithm
intervals
Results
172.0ms104×body1280valid
57.0ms21×body2560valid
46.0ms52×body640valid
19.0ms28×body320valid
10.0ms35×body80valid
7.0ms16×body160valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize54.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (tan (+ x eps)) (tan x))
3.9b
(tan (+ x eps))

rewrite70.0ms

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:
52.0ms
(- (tan (+ x eps)) (tan x))
15.0ms
(tan (+ x eps))

series413.0ms

Counts
2 → 6
Calls
2 calls:
230.0ms
(- (tan (+ x eps)) (tan x))
183.0ms
(tan (+ x eps))

simplify4.1s

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

prune526.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize141.0ms

Local error

Found 4 expressions with local error:

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

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×tan-quot
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
4×insert-posit16
3×associate-*r* associate-*l*
2×sub-neg flip3-- diff-log flip-- difference-of-squares
1×frac-times +-commutative sum-log flip3-+ times-frac pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-+ distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
4 → 66
Calls
4 calls:
21.0ms
(- 1 (* (tan x) (tan eps)))
38.0ms
(+ (tan x) (tan eps))
48.0ms
(* (tan x) (tan eps))
259.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series2.0s

Counts
4 → 12
Calls
4 calls:
270.0ms
(- 1 (* (tan x) (tan eps)))
251.0ms
(+ (tan x) (tan eps))
242.0ms
(* (tan x) (tan eps))
1.2s
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify5.7s

Counts
78 → 78
Iterations
IterNodes
done5002
33125
2989
1362
0149

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize299.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (cos eps))
0.2b
(* (sin eps) (/ (sin x) (cos eps)))
0.2b
(* (sin eps) (/ (sin x) (cos eps)))
3.1b
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite656.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
42×times-frac
39×*-un-lft-identity
28×add-cube-cbrt
26×associate-*r*
16×add-cbrt-cube add-exp-log
8×pow1
6×associate-*l* add-log-exp difference-of-squares
4×prod-exp cbrt-unprod insert-posit16 distribute-lft-out-- unswap-sqr
3×cbrt-undiv associate-/r* div-exp div-inv associate-/l*
2×pow-prod-down associate-*r/ *-commutative
1×clear-num sub-neg frac-2neg flip3-- diff-log frac-sub flip--
Counts
4 → 117
Calls
4 calls:
43.0ms
(/ (sin x) (cos eps))
62.0ms
(* (sin eps) (/ (sin x) (cos eps)))
76.0ms
(* (sin eps) (/ (sin x) (cos eps)))
458.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (sin x) (cos eps))
168.0ms
(* (sin eps) (/ (sin x) (cos eps)))
163.0ms
(* (sin eps) (/ (sin x) (cos eps)))
656.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify7.2s

Counts
129 → 129
Iterations
IterNodes
done5013
34170
21357
1424
0177

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize569.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin eps) (/ (sin x) (cos eps)))
0.3b
(* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
3.0b
(- (* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x))))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

rewrite941.0ms

Algorithm
rewrite-expression-head
Rules
684×times-frac
526×*-un-lft-identity
501×add-sqr-sqrt
292×add-cube-cbrt
123×swap-sqr
110×associate-*r*
105×difference-of-squares
100×associate-*l*
78×distribute-lft-out--
57×add-cbrt-cube add-exp-log
37×div-inv
23×cbrt-undiv div-exp
20×pow1
15×prod-exp cbrt-unprod unswap-sqr
9×associate-*r/ frac-sub
8×frac-times associate-*l/ associate-/r/
6×add-log-exp
5×flip3-- flip--
4×insert-posit16
3×pow-prod-down *-commutative
2×pow2 pow-plus pow-sqr pow-prod-up
1×sub-neg diff-log
Counts
4 → 446
Calls
4 calls:
59.0ms
(* (sin eps) (/ (sin x) (cos eps)))
558.0ms
(* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))))
71.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
144.0ms
(- (* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x))))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

series1.8s

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (sin eps) (/ (sin x) (cos eps)))
570.0ms
(* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))))
151.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
897.0ms
(- (* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x))))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

simplify5.6s

Counts
458 → 458
Iterations
IterNodes
done5001
12728
0714

prune6.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.1b

regimes579.0ms

Accuracy

0% (0.3b remaining)

Error of 12.5b against oracle of 12.1b and baseline of 12.5b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done26
126
020

end0.0ms

sample9.4s

Algorithm
intervals
Results
4.1s3245×body1280valid
2.3s1924×body640valid
1.5s617×body2560valid
930.0ms760×body320valid
183.0ms1085×body80valid
109.0ms369×body160valid