Details

Time bar (total: 28.5s)

sample487.0ms

Algorithm
intervals
Results
181.0ms88×body1280valid
130.0ms27×body2560valid
78.0ms62×body640valid
65.0ms28×body320valid
10.0ms39×body80valid
7.0ms12×body160valid

simplify17.0ms

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize28.0ms

Local error

Found 2 expressions with local error:

4.7b
(tan (+ x eps))
1.2b
(- (tan (+ x eps)) (tan x))

rewrite38.0ms

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:
Slowest
27.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series217.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
134.0ms
(- (tan (+ x eps)) (tan x))
83.0ms
(tan (+ x eps))

simplify1.2s

Counts
33 → 33

prune337.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize43.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))

rewrite147.0ms

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:
Slowest
93.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
24.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms
(+ (tan x) (tan eps))
14.0ms
(* (tan x) (tan eps))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
528.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
358.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
160.0ms
(* (tan x) (tan eps))
139.0ms
(+ (tan x) (tan eps))

simplify1.4s

Counts
102 → 102

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize47.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.1b
(+ (tan x) (tan eps))

rewrite142.0ms

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:
Slowest
51.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
48.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))
33.0ms
(* (tan x) (tan eps))
7.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
524.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))
262.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
142.0ms
(* (tan x) (tan eps))
134.0ms
(+ (tan x) (tan eps))

simplify784.0ms

Counts
115 → 115

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize37.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps))))) (tan x))
0.2b
(* (tan x) (sin eps))
0.2b
(/ (* (tan x) (sin eps)) (cos eps))
0.1b
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
31×*-un-lft-identity
27×associate-*r*
23×times-frac
20×add-exp-log
19×add-cube-cbrt
18×tan-quot
16×add-cbrt-cube
8×pow1 associate-*l/ frac-sub
7×associate-*l*
6×frac-times prod-exp add-log-exp difference-of-squares
4×flip3-+ div-exp frac-add cbrt-unprod flip-+ insert-posit16 unswap-sqr
3×cbrt-undiv associate-/r* distribute-lft-out--
2×flip3-- pow-prod-down associate-*r/ associate-/r/ un-div-inv *-commutative div-inv flip--
1×rec-exp clear-num sub-neg frac-2neg diff-log 1-exp distribute-lft-out associate-/l* associate-/l/
Counts
4 → 119
Calls
4 calls:
Slowest
70.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))
63.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps))))) (tan x))
14.0ms
(/ (* (tan x) (sin eps)) (cos eps))
13.0ms
(* (tan x) (sin eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
492.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps))))) (tan x))
264.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))
137.0ms
(/ (* (tan x) (sin eps)) (cos eps))
117.0ms
(* (tan x) (sin eps))

simplify1.2s

Counts
131 → 131

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

regimes242.0ms

Accuracy

89.9% (0.8b remaining)

Error of 15.0b against oracle of 14.2b and baseline of 21.7b

bsearch443.0ms

end0.0ms

sample14.0s

Algorithm
intervals
Results
6.8s3314×body1280valid
3.3s1875×body640valid
2.4s635×body2560valid
702.0ms748×body320valid
259.0ms1058×body80valid
226.0ms370×body160valid