Details

Time bar (total: 26.8s)

sample314.0ms

Algorithm
intervals
Results
165.0ms109×body1280valid
58.0ms20×body2560valid
48.0ms56×body640valid
14.0ms26×body320valid
7.0ms37×body80valid
3.0ms8×body160valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (tan (+ x eps)) (tan x))
3.7b
(tan (+ x eps))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×tan-quot add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u tan-sum frac-sub add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
43.0ms
(- (tan (+ x eps)) (tan x))
43.0ms
(tan (+ x eps))

series219.0ms

Counts
2 → 6
Calls
2 calls:
122.0ms
(- (tan (+ x eps)) (tan x))
97.0ms
(tan (+ x eps))

simplify2.7s

Counts
47 → 47
Iterations

Useful iterations: done (2.7s)

IterNodesCost
094720
1194597
2457510
31461450
done5000438

prune202.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.4b

localize30.0ms

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))))
0.3b
(* (tan x) (tan eps))
2.7b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
73×add-sqr-sqrt
66×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
9×tan-quot
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1 flip3-- flip--
5×div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-def associate-*r* associate-*l* associate-/r* associate-/l/
2×flip3-+ frac-add 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 distribute-lft-out-- unswap-sqr
Counts
4 → 169
Calls
4 calls:
9.0ms
(+ (tan x) (tan eps))
44.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
34.0ms
(* (tan x) (tan eps))
150.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
146.0ms
(+ (tan x) (tan eps))
305.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
125.0ms
(* (tan x) (tan eps))
521.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.7s

Counts
181 → 181
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02404762
15603970
215563555
done50003149

prune652.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan eps))
0.3b
(* (tan x) (tan eps))
0.3b
(pow (* (tan x) (tan eps)) 3)
2.4b
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×tan-quot
11×pow1 add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cube-div frac-times pow-unpow associate-*r/ pow-prod-down associate-*l/ prod-exp cbrt-unprod
2×pow-pow pow-exp *-commutative rem-cube-cbrt unswap-sqr
1×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod fma-udef sqr-pow
Counts
4 → 83
Calls
4 calls:
31.0ms
(* (tan x) (tan eps))
16.0ms
(* (tan x) (tan eps))
21.0ms
(pow (* (tan x) (tan eps)) 3)
1.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

series2.0s

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (tan x) (tan eps))
123.0ms
(* (tan x) (tan eps))
229.0ms
(pow (* (tan x) (tan eps)) 3)
1.5s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

simplify1.4s

Counts
95 → 95
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01771768
15041501
223011328
done50001320

prune760.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize166.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (* (cos x) (cos eps)) 3)
0.5b
(pow (* (cos x) (cos eps)) 3)
0.5b
(pow (* (cos x) (cos eps)) 3)
1.9b
(- (/ (sin x) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))) (cos x))) (/ (sin x) (cos x)))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
131×times-frac
117×prod-diff
107×*-un-lft-identity
105×add-sqr-sqrt
100×add-cube-cbrt
28×associate-*l/ associate-/r/
25×div-inv
15×flip3-- flip--
13×pow1 add-exp-log add-cbrt-cube
9×pow-unpow fma-neg
6×pow-pow pow-exp add-log-exp rem-cube-cbrt
4×expm1-log1p-u distribute-rgt-out-- log1p-expm1-u
3×cube-div cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod pow-prod-down prod-exp cos-mult cbrt-unprod sqr-pow
2×distribute-lft-out-- difference-of-squares
1×sub-neg diff-log frac-sub
Counts
4 → 224
Calls
4 calls:
14.0ms
(pow (* (cos x) (cos eps)) 3)
16.0ms
(pow (* (cos x) (cos eps)) 3)
15.0ms
(pow (* (cos x) (cos eps)) 3)
195.0ms
(- (/ (sin x) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))) (cos x))) (/ (sin x) (cos x)))

series700.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(pow (* (cos x) (cos eps)) 3)
115.0ms
(pow (* (cos x) (cos eps)) 3)
101.0ms
(pow (* (cos x) (cos eps)) 3)
395.0ms
(- (/ (sin x) (* (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))) (cos x))) (/ (sin x) (cos x)))

simplify1.8s

Counts
236 → 236
Iterations

Useful iterations: done (1.8s)

IterNodesCost
032012320
176211112
222698721
done50007543

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes333.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify15.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
047201
161199
done61199

end0.0ms

sample9.9s

Algorithm
intervals
Results
5.1s3297×body1280valid
1.8s663×body2560valid
1.5s1870×body640valid
801.0ms760×body320valid
196.0ms332×body160valid
194.0ms1078×body80valid