Details

Time bar (total: 30.0s)

sample315.0ms

Algorithm
intervals
Results
151.0ms114×body1280valid
57.0ms21×body2560valid
44.0ms53×body640valid
37.0ms26×body320valid
5.0ms29×body80valid
5.0ms13×body160valid

simplify5.0ms

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: 41.4b

localize56.0ms

Local error

Found 2 expressions with local error:

1.7b
(- (tan (+ x eps)) (tan x))
3.6b
(tan (+ x eps))

rewrite45.0ms

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))
14.0ms
(tan (+ x eps))

series211.0ms

Counts
2 → 6
Calls
2 calls:
132.0ms
(- (tan (+ x eps)) (tan x))
79.0ms
(tan (+ x eps))

simplify885.0ms

Counts
47 → 47
Iterations

Useful iterations: done (883.0ms)

IterNodesCost
094720
1202600
2741510
done5001450

prune215.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.2b

localize14.0ms

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))
0.3b
(* (tan x) (tan eps))
4.0b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite255.0ms

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:
56.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
18.0ms
(+ (tan x) (tan eps))
19.0ms
(* (tan x) (tan eps))
143.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
305.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
133.0ms
(+ (tan x) (tan eps))
129.0ms
(* (tan x) (tan eps))
566.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.2s

Counts
181 → 181
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02404762
15963988
228923557
done50003556

prune692.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.1b

localize28.0ms

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)
4.0b
(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)))

rewrite60.0ms

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:
16.0ms
(* (tan x) (tan eps))
27.0ms
(* (tan x) (tan eps))
13.0ms
(pow (* (tan x) (tan eps)) 3)
0.0ms
(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)))

series1.9s

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (tan x) (tan eps))
128.0ms
(* (tan x) (tan eps))
192.0ms
(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)))

simplify2.0s

Counts
95 → 95
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01741612
15421475
236101328
done50001324

prune631.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.4b

localize141.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (* (cos x) (cos eps)) 3)
0.6b
(pow (* (cos x) (cos eps)) 3)
0.6b
(pow (* (cos x) (cos eps)) 3)
3.8b
(- (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)))

rewrite487.0ms

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:
409.0ms
(pow (* (cos x) (cos eps)) 3)
17.0ms
(pow (* (cos x) (cos eps)) 3)
18.0ms
(pow (* (cos x) (cos eps)) 3)
31.0ms
(- (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)))

series2.2s

Counts
4 → 12
Calls
4 calls:
84.0ms
(pow (* (cos x) (cos eps)) 3)
89.0ms
(pow (* (cos x) (cos eps)) 3)
95.0ms
(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)))

simplify2.3s

Counts
147 → 147
Iterations

Useful iterations: 2 (549.0ms)

IterNodesCost
026716429
175215793
2414013295
done500013295

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

regimes250.0ms

Accuracy

91.4% (1.3b remaining)

Error of 6.0b against oracle of 4.8b and baseline of 19.8b

bsearch500.0ms

Steps
ItersRangePoint
7
1.6370258786577013e-44
3.9640321267410946e-42
6.7262813426299775e-43
9
-8.91844618026245e-89
-2.4994130436085512e-95
-8.784974285695472e-89

simplify15.0ms

Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
059399
174229
done74229

end0.0ms

sample11.3s

Algorithm
intervals
Results
4.9s3327×body1280valid
2.6s647×body2560valid
2.2s1853×body640valid
875.0ms737×body320valid
255.0ms1075×body80valid
117.0ms361×body160valid