Details

Time bar (total: 29.4s)

sample314.0ms

Algorithm
intervals
Results
159.0ms106×body1280valid
75.0ms53×body640valid
31.0ms11×body2560valid
17.0ms27×body320valid
8.0ms44×body80valid
6.0ms15×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize10.0ms

Local error

Found 2 expressions with local error:

1.7b
(- (tan (+ x eps)) (tan x))
3.9b
(tan (+ x eps))

rewrite93.0ms

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:
85.0ms
(- (tan (+ x eps)) (tan x))
7.0ms
(tan (+ x eps))

series222.0ms

Counts
2 → 6
Calls
2 calls:
152.0ms
(- (tan (+ x eps)) (tan x))
70.0ms
(tan (+ x eps))

simplify824.0ms

Counts
47 → 47
Iterations

Useful iterations: done (822.0ms)

IterNodesCost
094720
1202600
2741510
done5001450

prune180.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.9b

localize16.0ms

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

rewrite266.0ms

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))))
31.0ms
(* (tan x) (tan eps))
174.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
151.0ms
(+ (tan x) (tan eps))
317.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
133.0ms
(* (tan x) (tan eps))
520.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.3s

Counts
181 → 181
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02404762
15963988
228923557
done50003556

prune726.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.7b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.3b
(pow (* (tan x) (tan eps)) 3)
2.1b
(fma (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (fma (* (tan x) (tan eps)) (fma (tan x) (tan eps) 1) 1) (- (tan x)))

rewrite69.0ms

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:
33.0ms
(* (tan x) (tan eps))
19.0ms
(* (tan x) (tan eps))
14.0ms
(pow (* (tan x) (tan eps)) 3)
1.0ms
(fma (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (fma (* (tan x) (tan eps)) (fma (tan x) (tan eps) 1) 1) (- (tan x)))

series1.8s

Counts
4 → 12
Calls
4 calls:
125.0ms
(* (tan x) (tan eps))
136.0ms
(* (tan x) (tan eps))
187.0ms
(pow (* (tan x) (tan eps)) 3)
1.4s
(fma (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (fma (* (tan x) (tan eps)) (fma (tan x) (tan eps) 1) 1) (- (tan x)))

simplify2.2s

Counts
95 → 95
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01741612
15421475
236101328
done50001324

prune685.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.0b

localize182.0ms

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)
2.1b
(- (fma (/ (pow (sin eps) 3) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin x) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (+ (fma (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (/ (sin eps) (* (cos eps) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))))) (/ (sin x) (cos x)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
44×*-un-lft-identity
42×add-cube-cbrt
39×prod-diff
28×times-frac
13×pow1 add-exp-log add-cbrt-cube
9×pow-unpow
6×pow-pow pow-exp add-log-exp rem-cube-cbrt
4×expm1-log1p-u log1p-expm1-u
3×cube-div cube-mult pow-to-exp unpow-prod-down fma-neg unpow3 cube-prod pow-prod-down prod-exp cos-mult cbrt-unprod div-inv sqr-pow
2×difference-of-squares
1×sub-neg flip3-- diff-log associate--l+ flip-- fma-udef distribute-lft-out--
Counts
4 → 135
Calls
4 calls:
8.0ms
(pow (* (cos x) (cos eps)) 3)
8.0ms
(pow (* (cos x) (cos eps)) 3)
17.0ms
(pow (* (cos x) (cos eps)) 3)
32.0ms
(- (fma (/ (pow (sin eps) 3) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin x) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (+ (fma (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (/ (sin eps) (* (cos eps) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))))) (/ (sin x) (cos x)))

series2.3s

Counts
4 → 12
Calls
4 calls:
100.0ms
(pow (* (cos x) (cos eps)) 3)
111.0ms
(pow (* (cos x) (cos eps)) 3)
117.0ms
(pow (* (cos x) (cos eps)) 3)
2.0s
(- (fma (/ (pow (sin eps) 3) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin x) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (+ (fma (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (/ (sin eps) (* (cos eps) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))))) (/ (sin x) (cos x)))

simplify2.5s

Counts
147 → 147
Iterations

Useful iterations: 2 (688.0ms)

IterNodesCost
026716429
175215793
2414013295
done500013295

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

regimes389.0ms

Accuracy

91.5% (1.3b remaining)

Error of 6.4b against oracle of 5.1b and baseline of 19.9b

bsearch342.0ms

Steps
ItersRangePoint
6
5.011969102090218e-65
5.1113811756548066e-64
5.0315565590148686e-64
4
-6.51097445607371e-73
-4.28189121016468e-73
-5.57815376610615e-73

simplify16.0ms

Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
058397
175228
done75228

end0.0ms

sample10.8s

Algorithm
intervals
Results
5.1s3367×body1280valid
2.8s1778×body640valid
1.7s648×body2560valid
482.0ms769×body320valid
158.0ms1094×body80valid
111.0ms344×body160valid