Details

Time bar (total: 58.5s)

sample428.0ms

Algorithm
intervals
Results
181.0ms88×body1280valid
99.0ms62×body640valid
97.0ms27×body2560valid
20.0ms28×body320valid
9.0ms39×body80valid
6.0ms12×body160valid

simplify17.0ms

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize28.0ms

Local error

Found 2 expressions with local error:

4.7b
(tan (+ x eps))
1.2b
(- (tan (+ x eps)) (tan x))

rewrite38.0ms

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
27.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series210.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
127.0ms
(- (tan (+ x eps)) (tan x))
83.0ms
(tan (+ x eps))

simplify1.5s

Counts
49 → 49

prune452.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.0b

localize21.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))

rewrite209.0ms

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
113.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
48.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
27.0ms
(* (tan x) (tan eps))
14.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
518.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
298.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
141.0ms
(* (tan x) (tan eps))
128.0ms
(+ (tan x) (tan eps))

simplify775.0ms

Counts
185 → 185

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize56.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (/ (/ (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)))
0.1b
(/ (sin x) (cos x))

rewrite167.0ms

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
79.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
24.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
22.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
8.0ms
(/ (sin x) (cos x))

series599.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
300.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
141.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
131.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
28.0ms
(/ (sin x) (cos x))

simplify1.9s

Counts
803 → 803

prune15.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.0b

localize95.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (/ (/ (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))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b
(/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
2652×times-frac
1984×add-sqr-sqrt
1957×*-un-lft-identity
1400×add-cube-cbrt
1092×prod-diff
370×difference-of-squares
186×div-inv distribute-lft-out--
84×fma-neg
30×add-cbrt-cube add-exp-log
28×associate-/r/
26×associate-*l*
16×associate-*r*
15×flip3-- flip--
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
6×add-log-exp unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* associate-*l/
2×pow-prod-down *-commutative
1×frac-times clear-num sub-neg frac-2neg diff-log associate-*r/ frac-sub associate-/l* associate-/l/
Counts
4 → 1316
Calls
4 calls:
Slowest
137.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (/ (sin x) (cos x)))
19.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
18.0ms
(/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps))
15.0ms
(* (/ (sin x) (cos x)) (sin eps))

series690.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
305.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (/ (sin x) (cos x)))
167.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
133.0ms
(/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps))
85.0ms
(* (/ (sin x) (cos x)) (sin eps))

simplify3.1s

Counts
1328 → 1328

prune20.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

regimes129.0ms

Accuracy

0% (0.4b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 12.7b

bsearch6.0ms

end0.0ms

sample9.3s

Algorithm
intervals
Results
4.8s3314×body1280valid
1.6s635×body2560valid
1.5s1875×body640valid
636.0ms748×body320valid
364.0ms370×body160valid
179.0ms1058×body80valid