Details

Time bar (total: 27.5s)

sample305.0ms

Algorithm
intervals
Results
150.0ms106×body1280valid
82.0ms28×body2560valid
42.0ms58×body640valid
11.0ms23×body320valid
4.0ms31×body80valid
4.0ms10×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: 40.4b

localize46.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (tan (+ x eps)) (tan x))
4.5b
(tan (+ x eps))

rewrite38.0ms

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:
30.0ms
(- (tan (+ x eps)) (tan x))
7.0ms
(tan (+ x eps))

series227.0ms

Counts
2 → 6
Calls
2 calls:
135.0ms
(- (tan (+ x eps)) (tan x))
92.0ms
(tan (+ x eps))

simplify2.4s

Counts
47 → 47
Iterations

Useful iterations: done (2.4s)

IterNodesCost
094720
1194597
2457510
31461450
done5000438

prune133.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
2.8b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite228.0ms

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:
37.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms
(+ (tan x) (tan eps))
30.0ms
(* (tan x) (tan eps))
135.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
288.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
161.0ms
(+ (tan x) (tan eps))
118.0ms
(* (tan x) (tan eps))
624.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.8s

Counts
181 → 181
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02404762
15603970
215583555
done50003149

prune620.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (tan x) (- (tan eps)) 1)
0.1b
(/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1))
0.2b
(+ (tan eps) (tan x))
2.8b
(- (/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1)) (tan x))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
67×add-sqr-sqrt
62×add-cube-cbrt
61×times-frac
48×prod-diff
17×distribute-lft-out
16×fma-neg
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×tan-quot div-inv
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-def associate-/r* associate-/l/
2×flip3-+ frac-add flip-+ difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log frac-sub flip-- fma-udef distribute-lft-out--
Counts
4 → 146
Calls
4 calls:
0.0ms
(fma (tan x) (- (tan eps)) 1)
30.0ms
(/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1))
15.0ms
(+ (tan eps) (tan x))
81.0ms
(- (/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1)) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
179.0ms
(fma (tan x) (- (tan eps)) 1)
325.0ms
(/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1))
143.0ms
(+ (tan eps) (tan x))
577.0ms
(- (/ (+ (tan eps) (tan x)) (fma (tan x) (- (tan eps)) 1)) (tan x))

simplify2.8s

Counts
158 → 158
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01974292
14423635
211413246
339792811
done50002811

prune639.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(pow (* (tan x) (tan eps)) 3)
2.9b
(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)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
40×tan-quot
21×add-exp-log add-cbrt-cube
19×frac-times pow-prod-down
13×associate-*r/ associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u associate-*r* associate-*l* pow-sqr pow-prod-up log1p-expm1-u add-log-exp
3×cube-div pow-unpow
2×pow-pow pow-plus pow-exp *-commutative rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod swap-sqr fma-udef unswap-sqr sqr-pow
Counts
4 → 111
Calls
4 calls:
15.0ms
(* (tan x) (tan eps))
87.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
36.0ms
(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)))

series1.8s

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (tan x) (tan eps))
182.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
204.0ms
(pow (* (tan x) (tan eps)) 3)
1.3s
(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)))

simplify1.6s

Counts
123 → 123
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02342288
16581831
229631614
done50021583

prune629.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.0b

regimes208.0ms

Accuracy

75.5% (1.8b remaining)

Error of 14.2b against oracle of 12.3b and baseline of 19.9b

bsearch325.0ms

Steps
ItersRangePoint
4
8.374626897052483e-75
1.4393546628418213e-74
9.730491097206055e-75
8
-2.286418009881596e-145
-4.6651284413305015e-148
-2.0348245825395098e-145

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
050329
162174
done62174

end0.0ms

sample10.9s

Algorithm
intervals
Results
6.4s3328×body1280valid
1.8s625×body2560valid
1.6s1824×body640valid
504.0ms817×body320valid
216.0ms1052×body80valid
153.0ms354×body160valid