Details

Time bar (total: 10.7s)

sample159.0ms

Algorithm
intervals
Results
73.0ms98×body1280valid
40.0ms24×body2560valid
23.0ms62×body640valid
6.0ms25×body320valid
3.0ms33×body80valid
2.0ms14×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104
done104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b
(- (tan (+ x eps)) (tan x))
5.2b
(tan (+ x eps))

rewrite25.0ms

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:
18.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series151.0ms

Counts
2 → 6
Calls
2 calls:
94.0ms
(- (tan (+ x eps)) (tan x))
57.0ms
(tan (+ x eps))

simplify72.0ms

Counts
47 → 47
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0192420
1538319
22593310
35001255
done5001255

prune122.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
4.7b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite155.0ms

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:
28.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms
(+ (tan x) (tan eps))
17.0ms
(* (tan x) (tan eps))
95.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series790.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
95.0ms
(+ (tan x) (tan eps))
97.0ms
(* (tan x) (tan eps))
375.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify75.0ms

Counts
181 → 181
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05592923
120542373
250012349
done50012349

prune410.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.4b
(pow (* (tan x) (tan eps)) 3)
4.7b
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

rewrite46.0ms

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:
17.0ms
(* (tan x) (tan eps))
15.0ms
(* (tan x) (tan eps))
12.0ms
(pow (* (tan x) (tan eps)) 3)
0.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (tan x) (tan eps))
97.0ms
(* (tan x) (tan eps))
130.0ms
(pow (* (tan x) (tan eps)) 3)
923.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

simplify69.0ms

Counts
95 → 95
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0489922
12636827
25002826
done5002826

prune474.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin x) 3)
0.4b
(pow (sin x) 3)
0.4b
(pow (sin x) 3)
2.4b
(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
131×times-frac
117×prod-diff
113×*-un-lft-identity
111×add-sqr-sqrt
106×add-cube-cbrt
28×associate-*l/ associate-/r/
25×div-inv
15×flip3-- flip--
9×unpow-prod-down pow-unpow fma-neg cube-prod
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
4×expm1-log1p-u distribute-rgt-out-- log1p-expm1-u
3×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
2×distribute-lft-out-- difference-of-squares
1×sub-neg diff-log frac-sub
Counts
4 → 224
Calls
4 calls:
4.0ms
(pow (sin x) 3)
4.0ms
(pow (sin x) 3)
4.0ms
(pow (sin x) 3)
110.0ms
(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sin x) 3)
37.0ms
(pow (sin x) 3)
30.0ms
(pow (sin x) 3)
262.0ms
(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

simplify135.0ms

Counts
236 → 236
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
07418002
131605750
250035716
done50035716

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes199.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
070120
170120
done70120

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.3s3282×body1280valid
1.1s646×body2560valid
732.0ms1854×body640valid
210.0ms761×body320valid
92.0ms1086×body80valid
62.0ms371×body160valid