Details

Time bar (total: 41.5s)

sample484.0ms

Algorithm
intervals
Results
268.0ms103×body1280valid
86.0ms22×body2560valid
69.0ms52×body640valid
30.0ms31×body320valid
12.0ms41×body80valid
4.0ms7×body160valid

simplify8.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize17.0ms

Local error

Found 2 expressions with local error:

4.5b
(tan (+ x eps))
0.9b
(- (tan (+ x eps)) (tan x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×tan-quot add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 tan-sum add-cbrt-cube add-exp-log frac-sub insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
Slowest
15.0ms
(- (tan (+ x eps)) (tan x))
8.0ms
(tan (+ x eps))

series228.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
159.0ms
(- (tan (+ x eps)) (tan x))
69.0ms
(tan (+ x eps))

simplify1.5s

Counts
49 → 49

prune519.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.9b

localize30.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite169.0ms

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-cbrt-cube add-exp-log add-log-exp
6×pow1 flip3-- flip--
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* fma-def associate-*r* associate-*l* associate-/l/
2×flip3-+ frac-add flip-+ difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 173
Calls
4 calls:
Slowest
96.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
42.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms
(* (tan x) (tan eps))
8.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
544.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
336.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
131.0ms
(+ (tan x) (tan eps))
130.0ms
(* (tan x) (tan eps))

simplify679.0ms

Counts
185 → 185

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.0b

localize82.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b
(/ (sin x) (cos x))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
1393×times-frac
890×add-sqr-sqrt
851×*-un-lft-identity
845×add-cube-cbrt
585×prod-diff
106×div-inv
45×fma-neg
30×add-cbrt-cube add-exp-log
28×associate-/r/
26×associate-*r* associate-*l*
15×flip3-- flip--
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod unswap-sqr
6×add-log-exp difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* associate-/l*
2×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative distribute-lft-out--
1×quot-tan clear-num sub-neg frac-2neg diff-log frac-sub
Counts
4 → 791
Calls
4 calls:
Slowest
91.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
38.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
20.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
12.0ms
(/ (sin x) (cos x))

series619.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
303.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
148.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
131.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
37.0ms
(/ (sin x) (cos x))

simplify2.1s

Counts
803 → 803

prune16.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.0b

localize80.0ms

Local error

Found 4 expressions with local error:

3.4b
(fma (/ (/ (sin x) (cos x)) (- (* 1 1) (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (- (/ (sin x) (cos x))))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
158×add-cbrt-cube add-exp-log
73×prod-exp cbrt-unprod
56×add-sqr-sqrt
48×cbrt-undiv div-exp
47×pow1
44×times-frac
32×*-un-lft-identity add-cube-cbrt
27×associate-*r* associate-*l*
19×frac-times pow-prod-down
13×associate-*l/ associate-*r/
8×unswap-sqr
4×expm1-log1p-u pow-sqr pow-prod-up insert-posit16 log1p-expm1-u div-inv add-log-exp
3×*-commutative
2×pow-plus
1×pow2 swap-sqr fma-udef
Counts
4 → 211
Calls
4 calls:
Slowest
71.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
34.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
25.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.0ms
(fma (/ (/ (sin x) (cos x)) (- (* 1 1) (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (- (/ (sin x) (cos x))))

series932.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
552.0ms
(fma (/ (/ (sin x) (cos x)) (- (* 1 1) (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (- (/ (sin x) (cos x))))
148.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
118.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
114.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))

simplify1.3s

Counts
223 → 223

prune2.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.0b

regimes181.0ms

Accuracy

0% (0.4b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch5.0ms

end0.0ms

sample9.9s

Algorithm
intervals
Results
5.4s3374×body1280valid
1.9s1779×body640valid
1.6s648×body2560valid
434.0ms749×body320valid
201.0ms1100×body80valid
142.0ms350×body160valid