Details

Time bar (total: 14.5s)

sample168.0ms

Algorithm
intervals
Results
85.0ms111×body1280valid
39.0ms24×body2560valid
22.0ms55×body640valid
9.0ms32×body320valid
2.0ms26×body80valid
1.0ms8×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b
(- (tan (+ x eps)) (tan x))
4.0b
(tan (+ x eps))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×tan-quot add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt tan-sum frac-sub add-cbrt-cube
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 25
Calls
2 calls:
7.0ms
(- (tan (+ x eps)) (tan x))
3.0ms
(tan (+ x eps))

series139.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(- (tan (+ x eps)) (tan x))
54.0ms
(tan (+ x eps))

simplify930.0ms

Counts
31 → 31
Iterations

Useful iterations: 4 (270.0ms)

IterNodesCost
068367
1135355
2288341
3573337
41618335
done5001335

prune86.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

localize11.0ms

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))
2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite64.0ms

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-exp-log add-cbrt-cube add-log-exp
6×pow1
5×distribute-lft-out
4×associate-/l*
3×associate-*r* associate-*l* associate-/r* associate-/l/
2×flip3-- flip3-+ frac-add associate-/r/ flip-- flip-+ difference-of-squares
1×cbrt-undiv +-commutative frac-times sub-neg frac-2neg diff-log associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num sum-log *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 86
Calls
4 calls:
3.0ms
(+ (tan x) (tan eps))
11.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms
(* (tan x) (tan eps))
41.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series733.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(+ (tan x) (tan eps))
205.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms
(* (tan x) (tan eps))
349.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.3s

Counts
98 → 98
Iterations

Useful iterations: 3 (826.0ms)

IterNodesCost
01721724
13931649
211831579
346291563
done50001563

prune286.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.6b
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
33×add-exp-log add-cbrt-cube
11×add-sqr-sqrt *-un-lft-identity
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod add-log-exp
6×add-cube-cbrt times-frac
5×associate-/l*
4×pow1 associate-/r/
3×frac-2neg clear-num associate-/r* frac-sub div-inv
2×flip3-- diff-log associate-*l/ cos-mult flip-- associate-/l/ sin-mult distribute-lft-out-- difference-of-squares
1×sub-neg flip3-+ frac-add associate--l+ sum-log flip-+ distribute-lft-out
Counts
4 → 90
Calls
4 calls:
11.0ms
(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
5.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
6.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
249.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series708.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
95.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
97.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
375.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify652.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (200.0ms)

IterNodesCost
01933410
15433256
222172909
done50002909

prune386.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 15.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (* (cos eps) (/ (cos x) (sin eps))))
0.2b
(/ (cos x) (sin eps))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.6b
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (sin x) (* (cos eps) (/ (cos x) (sin eps))))) (cos eps)))) (/ (sin x) (cos x)))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
19×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt times-frac
9×cbrt-undiv div-exp add-log-exp
7×associate-/l*
6×prod-exp cbrt-unprod
5×associate-/r*
4×pow1
3×frac-2neg clear-num frac-sub div-inv
2×diff-log associate-/r/ distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip3-+ associate-*r/ frac-add associate--l+ sum-log cos-mult flip-- flip-+ associate-/l/ sin-mult distribute-lft-out
Counts
4 → 95
Calls
4 calls:
6.0ms
(/ (sin x) (* (cos eps) (/ (cos x) (sin eps))))
3.0ms
(/ (cos x) (sin eps))
6.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
242.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (sin x) (* (cos eps) (/ (cos x) (sin eps))))) (cos eps)))) (/ (sin x) (cos x)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (sin x) (* (cos eps) (/ (cos x) (sin eps))))
45.0ms
(/ (cos x) (sin eps))
96.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
367.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (sin x) (* (cos eps) (/ (cos x) (sin eps))))) (cos eps)))) (/ (sin x) (cos x)))

simplify938.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (235.0ms)

IterNodesCost
02403033
16332961
224882649
done50012649

prune387.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.1b

regimes256.0ms

Accuracy

89.1% (0.8b remaining)

Error of 15.5b against oracle of 14.6b and baseline of 22.3b

bsearch201.0ms

Steps
ItersRangePoint
11
2.28145452431431e-18
2231369.5462890854
2.855628566329288e-18
10
-4.161461817671002e-38
-2.4684106388071866e-48
-1.9500134694671836e-38

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02577
13948
done3948

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.5s3341×body1280valid
1.2s666×body2560valid
750.0ms1788×body640valid
216.0ms779×body320valid
98.0ms1078×body80valid
70.0ms348×body160valid