Details

Time bar (total: 16.5s)

sample164.0ms

Algorithm
intervals
Results
79.0ms102×body1280valid
37.0ms22×body2560valid
27.0ms65×body640valid
5.0ms20×body320valid
3.0ms37×body80valid
2.0ms10×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: 38.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b
(- (tan (+ x eps)) (tan x))
4.7b
(tan (+ x eps))

rewrite12.0ms

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))
4.0ms
(tan (+ x eps))

series150.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(- (tan (+ x eps)) (tan x))
59.0ms
(tan (+ x eps))

simplify2.0s

Counts
31 → 31
Iterations

Useful iterations: 4 (247.0ms)

IterNodesCost
068367
1135355
2288341
3540337
41249335
53284335
done5001335

prune92.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan eps) (tan x))
0.1b
(- 1 (* (tan eps) (tan x)))
0.2b
(* (tan eps) (tan x))
1.9b
(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×tan-quot
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l*
2×sub-neg flip3-- diff-log flip-- difference-of-squares
1×+-commutative frac-times flip3-+ times-frac associate-*r/ pow-prod-down associate-*l/ frac-add prod-exp sum-log *-commutative frac-sub cbrt-unprod flip-+ distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
4 → 62
Calls
4 calls:
3.0ms
(+ (tan eps) (tan x))
2.0ms
(- 1 (* (tan eps) (tan x)))
5.0ms
(* (tan eps) (tan x))
39.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

series683.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(+ (tan eps) (tan x))
106.0ms
(- 1 (* (tan eps) (tan x)))
93.0ms
(* (tan eps) (tan x))
392.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify1.8s

Counts
74 → 74
Iterations

Useful iterations: 3 (634.0ms)

IterNodesCost
01451093
13321049
2867991
32407976
done5000976

prune234.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (exp (- 1 (* (tan eps) (tan x)))))
0.2b
(exp (- 1 (* (tan eps) (tan x))))
0.2b
(* (tan eps) (tan x))
1.9b
(- (/ (+ (tan eps) (tan x)) (log (exp (- 1 (* (tan eps) (tan x)))))) (tan x))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×*-un-lft-identity
9×add-cube-cbrt add-log-exp
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
5×tan-quot log-prod
4×exp-sum log-pow
3×sub-neg associate-*r* associate-*l*
2×exp-diff diff-log rem-exp-log difference-of-squares
1×frac-times log-div flip3-- times-frac associate-*r/ rem-log-exp pow-prod-down associate-*l/ prod-exp *-commutative frac-sub flip-- cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
5.0ms
(log (exp (- 1 (* (tan eps) (tan x)))))
5.0ms
(exp (- 1 (* (tan eps) (tan x))))
5.0ms
(* (tan eps) (tan x))
68.0ms
(- (/ (+ (tan eps) (tan x)) (log (exp (- 1 (* (tan eps) (tan x)))))) (tan x))

series723.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(log (exp (- 1 (* (tan eps) (tan x)))))
141.0ms
(exp (- 1 (* (tan eps) (tan x))))
91.0ms
(* (tan eps) (tan x))
382.0ms
(- (/ (+ (tan eps) (tan x)) (log (exp (- 1 (* (tan eps) (tan x)))))) (tan x))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: 3 (420.0ms)

IterNodesCost
01471249
13101138
27911051
321471032
done50001032

prune254.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan eps) (tan x))
0.2b
(* (tan eps) (tan x))
0.3b
(pow (* (tan eps) (tan x)) 3)
1.9b
(- (/ (+ (tan eps) (tan x)) (/ (- 1 (pow (* (tan eps) (tan x)) 3)) (+ (* (* (tan eps) (tan x)) (+ 1 (* (tan eps) (tan x)))) 1))) (tan x))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
13×tan-quot
11×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
9×add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
3×cube-div frac-times pow-unpow times-frac associate-*r/ pow-prod-down associate-*l/ prod-exp cbrt-unprod difference-of-squares
2×pow-pow pow-exp *-commutative rem-cube-cbrt unswap-sqr
1×cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- diff-log unpow3 cube-prod frac-sub flip-- distribute-lft-out-- sqr-pow
Counts
4 → 84
Calls
4 calls:
5.0ms
(* (tan eps) (tan x))
5.0ms
(* (tan eps) (tan x))
4.0ms
(pow (* (tan eps) (tan x)) 3)
241.0ms
(- (/ (+ (tan eps) (tan x)) (/ (- 1 (pow (* (tan eps) (tan x)) 3)) (+ (* (* (tan eps) (tan x)) (+ 1 (* (tan eps) (tan x)))) 1))) (tan x))

series1.9s

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (tan eps) (tan x))
97.0ms
(* (tan eps) (tan x))
130.0ms
(pow (* (tan eps) (tan x)) 3)
1.6s
(- (/ (+ (tan eps) (tan x)) (/ (- 1 (pow (* (tan eps) (tan x)) 3)) (+ (* (* (tan eps) (tan x)) (+ 1 (* (tan eps) (tan x)))) 1))) (tan x))

simplify795.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (216.0ms)

IterNodesCost
01942105
15311971
224361821
done50011821

prune345.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.9b

regimes175.0ms

Accuracy

74.3% (1.9b remaining)

Error of 14.3b against oracle of 12.4b and baseline of 19.7b

bsearch311.0ms

Steps
ItersRangePoint
7
3.341779155283458e-77
2.208279242247018e-75
1.7108564194720778e-75
10
-2.1704013439664117e-145
-9.67835236051937e-157
-2.1409221632056665e-145

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
058357
183189
done83189

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.5s3332×body1280valid
1.1s654×body2560valid
781.0ms1879×body640valid
207.0ms731×body320valid
86.0ms1055×body80valid
63.0ms349×body160valid