Details

Time bar (total: 24.4s)

sample329.0ms

Algorithm
intervals
Results
199.0ms111×body1280valid
53.0ms20×body2560valid
39.0ms56×body640valid
11.0ms23×body320valid
6.0ms36×body80valid
4.0ms10×body160valid

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (tan (+ x eps)) (tan x))
2.4b
(tan (+ x eps))

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
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 25
Calls
2 calls:
14.0ms
(- (tan (+ x eps)) (tan x))
5.0ms
(tan (+ x eps))

series214.0ms

Counts
2 → 6
Calls
2 calls:
131.0ms
(- (tan (+ x eps)) (tan x))
83.0ms
(tan (+ x eps))

simplify922.0ms

Counts
31 → 31
Iterations
IterNodes
done5000
31176
2355
1137
068

prune204.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1 (* (tan x) (tan eps)))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b
(* (tan x) (tan eps))
2.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
8×add-cbrt-cube add-exp-log add-log-exp
7×tan-quot
6×pow1
4×distribute-lft-out associate-/l*
3×associate-/r* flip3-- associate-*r* associate-*l* flip-- associate-/l/
2×sub-neg diff-log associate-/r/ difference-of-squares
1×frac-times cbrt-undiv clear-num frac-2neg flip3-+ div-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-+ div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 85
Calls
4 calls:
4.0ms
(- 1 (* (tan x) (tan eps)))
33.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms
(* (tan x) (tan eps))
116.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
150.0ms
(- 1 (* (tan x) (tan eps)))
311.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
163.0ms
(* (tan x) (tan eps))
508.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.4s

Counts
97 → 97
Iterations
IterNodes
done5000
22002
1431
0171

prune685.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.9b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin eps) (cos eps))
0.2b
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
0.2b
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
3.5b
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps))))) (/ (sin x) (cos x)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
64×times-frac
46×*-un-lft-identity
40×add-cube-cbrt
30×add-cbrt-cube add-exp-log
26×associate-*r* associate-*l*
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod unswap-sqr
6×add-log-exp difference-of-squares
5×div-inv
3×associate-/r* associate-/l*
2×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative distribute-lft-out--
1×quot-tan clear-num sub-neg frac-2neg flip3-- diff-log frac-sub flip--
Counts
4 → 149
Calls
4 calls:
8.0ms
(/ (sin eps) (cos eps))
38.0ms
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
26.0ms
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
136.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps))))) (/ (sin x) (cos x)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (sin eps) (cos eps))
139.0ms
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
150.0ms
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
317.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps))))) (/ (sin x) (cos x)))

simplify2.0s

Counts
161 → 161
Iterations
IterNodes
done5000
23117
1609
0226

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.8b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (/ (sin eps) (cos x)) (sin x)) (/ 1 (cos eps)))
0.2b
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
0.2b
(* (/ (sin eps) (cos x)) (sin x))
3.5b
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin eps) (cos x)) (sin x)) (/ 1 (cos eps))))) (/ (sin x) (cos x)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
60×add-exp-log
52×times-frac
42×add-cbrt-cube
39×*-un-lft-identity
33×add-cube-cbrt
29×associate-*r*
27×associate-*l*
26×prod-exp
16×cbrt-unprod
15×div-exp
13×pow1
10×cbrt-undiv
6×add-log-exp difference-of-squares unswap-sqr
5×pow-prod-down associate-*l/
4×div-inv
3×rec-exp 1-exp *-commutative
2×frac-times associate-*r/ distribute-lft-out--
1×sub-neg flip3-- diff-log un-div-inv frac-sub flip--
Counts
4 → 149
Calls
4 calls:
55.0ms
(* (* (/ (sin eps) (cos x)) (sin x)) (/ 1 (cos eps)))
27.0ms
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
18.0ms
(* (/ (sin eps) (cos x)) (sin x))
109.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin eps) (cos x)) (sin x)) (/ 1 (cos eps))))) (/ (sin x) (cos x)))

series687.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (* (/ (sin eps) (cos x)) (sin x)) (/ 1 (cos eps)))
112.0ms
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
110.0ms
(* (/ (sin eps) (cos x)) (sin x))
334.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin eps) (cos x)) (sin x)) (/ 1 (cos eps))))) (/ (sin x) (cos x)))

simplify934.0ms

Counts
161 → 161
Iterations
IterNodes
done5001
1844
0283

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.8b

regimes286.0ms

Accuracy

0% (0.4b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done29
129
023

end0.0ms

sample11.4s

Algorithm
intervals
Results
6.1s3324×body1280valid
2.3s637×body2560valid
1.8s1870×body640valid
502.0ms731×body320valid
171.0ms1103×body80valid
113.0ms335×body160valid