Details

Time bar (total: 41.9s)

sample442.0ms

Algorithm
intervals
Results
230.0ms113×body1280valid
107.0ms20×body2560valid
59.0ms53×body640valid
18.0ms21×body320valid
9.0ms37×body80valid
7.0ms12×body160valid

simplify9.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize26.0ms

Local error

Found 2 expressions with local error:

3.8b
(tan (+ x eps))
1.0b
(- (tan (+ x eps)) (tan x))

rewrite31.0ms

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
20.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series218.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
126.0ms
(- (tan (+ x eps)) (tan x))
91.0ms
(tan (+ x eps))

simplify1.5s

Counts
49 → 49

prune500.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ (+ (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))))

rewrite145.0ms

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
83.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
25.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
18.0ms
(* (tan x) (tan eps))
14.0ms
(+ (tan x) (tan eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
510.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
276.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
131.0ms
(+ (tan x) (tan eps))
123.0ms
(* (tan x) (tan eps))

simplify747.0ms

Counts
185 → 185

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize42.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ (/ (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 eps) (cos eps))

rewrite184.0ms

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
80.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
36.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
34.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
8.0ms
(/ (sin eps) (cos eps))

series732.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
373.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
181.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
141.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
37.0ms
(/ (sin eps) (cos eps))

simplify2.3s

Counts
803 → 803

prune15.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.8b

localize63.0ms

Local error

Found 4 expressions with local error:

31.6b
(fma (- (/ 1 (cos x))) (sin x) (* (/ 1 (cos x)) (sin x)))
17.6b
(fma (/ (sin x) 1) (/ (/ 1 (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (* (/ 1 (cos x)) (sin x))))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
44×times-frac
32×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×associate-*r* associate-*l*
8×pow1 cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
2×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef
Counts
4 → 128
Calls
4 calls:
Slowest
28.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
18.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.0ms
(fma (- (/ 1 (cos x))) (sin x) (* (/ 1 (cos x)) (sin x)))
0.0ms
(fma (/ (sin x) 1) (/ (/ 1 (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (* (/ 1 (cos x)) (sin x))))

series688.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
300.0ms
(fma (/ (sin x) 1) (/ (/ 1 (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (* (/ 1 (cos x)) (sin x))))
168.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
144.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
75.0ms
(fma (- (/ 1 (cos x))) (sin x) (* (/ 1 (cos x)) (sin x)))

simplify642.0ms

Counts
140 → 140

prune2.0s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.8b

regimes185.0ms

Accuracy

0% (0.4b remaining)

Error of 13.1b against oracle of 12.7b and baseline of 13.1b

bsearch3.1s

end0.0ms

sample10.1s

Algorithm
intervals
Results
5.4s3278×body1280valid
2.0s1863×body640valid
1.7s667×body2560valid
507.0ms770×body320valid
177.0ms1103×body80valid
163.0ms319×body160valid