Details

Time bar (total: 2.4m)

sample345.0ms

Algorithm
intervals
Results
208.0ms112×body1280valid
55.0ms60×body640valid
48.0ms19×body2560valid
14.0ms24×body320valid
7.0ms33×body80valid
3.0ms8×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
310
210
19
06

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize53.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (tan (+ x eps)) (tan x))
2.8b
(tan (+ x eps))

rewrite41.0ms

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:
27.0ms
(- (tan (+ x eps)) (tan x))
12.0ms
(tan (+ x eps))

series185.0ms

Counts
2 → 6
Calls
2 calls:
120.0ms
(- (tan (+ x eps)) (tan x))
65.0ms
(tan (+ x eps))

simplify2.9s

Counts
49 → 49
Iterations
IterNodes
43889
31289
2437
1203
096

prune531.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1 (* (tan x) (tan eps)))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b
(* (tan x) (tan eps))
3.3b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
74×add-sqr-sqrt
67×add-cube-cbrt
61×times-frac
57×prod-diff
21×fma-neg
16×distribute-lft-out
10×associate-/r/
8×add-cbrt-cube add-exp-log add-log-exp
7×flip3-- tan-quot flip--
6×pow1
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×sub-neg diff-log difference-of-squares
1×frac-times cbrt-undiv clear-num frac-2neg flip3-+ div-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-+ distribute-lft-out-- unswap-sqr
Counts
4 → 175
Calls
4 calls:
11.0ms
(- 1 (* (tan x) (tan eps)))
31.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
17.0ms
(* (tan x) (tan eps))
95.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.5s

Counts
4 → 12
Calls
4 calls:
163.0ms
(- 1 (* (tan x) (tan eps)))
340.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
123.0ms
(* (tan x) (tan eps))
917.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.5s

Counts
187 → 187
Iterations
IterNodes
35052
21534
1591
0249

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos x) (/ (sin eps) (cos eps)))
0.3b
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
0.3b
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
4.5b
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (cos x) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))

rewrite500.0ms

Algorithm
rewrite-expression-head
Rules
8218×times-frac
7311×add-sqr-sqrt
4025×*-un-lft-identity
2922×add-cube-cbrt
2106×prod-diff
1462×difference-of-squares
383×div-inv
186×distribute-lft-out--
162×fma-neg
101×associate-/r*
39×associate-/r/
27×add-cbrt-cube add-exp-log
15×cbrt-undiv flip3-- div-exp flip--
9×associate-/l*
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
1×sub-neg diff-log frac-sub
Counts
4 → 2764
Calls
4 calls:
12.0ms
(/ (cos x) (/ (sin eps) (cos eps)))
13.0ms
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
17.0ms
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
280.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (cos x) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))

series766.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (cos x) (/ (sin eps) (cos eps)))
156.0ms
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
150.0ms
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
332.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (cos x) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))

simplify6.9s

Counts
2776 → 2776
Iterations
IterNodes
16453
02858

prune53.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos x) (/ (sin eps) (cos eps)))
0.3b
(/ (sin x) (/ (/ (cos x) (sin eps)) (/ 1 (cos eps))))
0.3b
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
4.5b
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (cos x) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))

rewrite456.0ms

Algorithm
rewrite-expression-head
Rules
9956×times-frac
8033×add-sqr-sqrt
4747×*-un-lft-identity
3644×add-cube-cbrt
2106×prod-diff
1462×difference-of-squares
475×div-inv
231×associate-/r*
186×distribute-lft-out--
162×fma-neg
50×add-exp-log
39×associate-/r/
36×add-cbrt-cube
34×div-exp
22×cbrt-undiv
15×flip3-- flip--
9×associate-/l*
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
2×rec-exp 1-exp
1×sub-neg diff-log frac-sub
Counts
4 → 3292
Calls
4 calls:
11.0ms
(/ (cos x) (/ (sin eps) (cos eps)))
17.0ms
(/ (sin x) (/ (/ (cos x) (sin eps)) (/ 1 (cos eps))))
15.0ms
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
234.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (cos x) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))

series522.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (cos x) (/ (sin eps) (cos eps)))
100.0ms
(/ (sin x) (/ (/ (cos x) (sin eps)) (/ 1 (cos eps))))
101.0ms
(/ (sin x) (/ (cos x) (/ (sin eps) (cos eps))))
246.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (cos x) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))

simplify15.6s

Counts
3304 → 3304
Iterations
IterNodes
110730
04238

prune48.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.3b

regimes201.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 12.8b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
222
122
020

end0.0ms

sample9.5s

Algorithm
intervals
Results
5.2s3368×body1280valid
1.7s593×body2560valid
1.7s1859×body640valid
484.0ms759×body320valid
192.0ms1101×body80valid
104.0ms320×body160valid