Details

Time bar (total: 42.2s)

sample488.0ms

Algorithm
intervals
Results
247.0ms111×body1280valid
115.0ms55×body640valid
81.0ms21×body2560valid
15.0ms19×body320valid
9.0ms35×body80valid
8.0ms15×body160valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
324
224
121
06

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize13.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (tan (+ x eps)) (tan x))
3.2b
(tan (+ x eps))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity tan-quot add-log-exp
2×pow1 tan-sum add-cbrt-cube add-exp-log frac-sub add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 27
Calls
2 calls:
26.0ms
(- (tan (+ x eps)) (tan x))
5.0ms
(tan (+ x eps))

series191.0ms

Counts
2 → 6
Calls
2 calls:
123.0ms
(- (tan (+ x eps)) (tan x))
67.0ms
(tan (+ x eps))

simplify1.1s

Counts
33 → 33
Iterations
IterNodes
52965
41565
3812
2440
1269
070

prune343.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b
(* (tan x) (tan eps))
3.5b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1
5×distribute-lft-out
4×insert-posit16 associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×flip3-+ flip3-- frac-add associate-/r/ flip-+ 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 div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 90
Calls
4 calls:
10.0ms
(+ (tan x) (tan eps))
23.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
13.0ms
(* (tan x) (tan eps))
54.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series874.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (tan x) (tan eps))
239.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
121.0ms
(* (tan x) (tan eps))
407.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.0s

Counts
102 → 102
Iterations
IterNodes
33604
21570
1708
0174

prune814.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 17.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (cos x))
0.3b
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
0.3b
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
3.5b
(- (+ (/ (/ (sin x) (cos x)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))))) (/ (sin x) (cos x)))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
864×times-frac
437×*-un-lft-identity
409×add-sqr-sqrt
404×add-cube-cbrt
59×div-inv
30×add-cbrt-cube add-exp-log
29×associate-/r* associate-/l*
17×cbrt-undiv div-exp
10×distribute-lft-out--
9×add-log-exp
5×distribute-lft-out
4×pow1 insert-posit16
3×clear-num frac-2neg frac-sub
2×diff-log associate-/r/ difference-of-squares associate-/l/
1×quot-tan sum-log sub-neg flip3-+ flip3-- frac-add associate--l+ flip-+ flip--
Counts
4 → 487
Calls
4 calls:
8.0ms
(/ (sin x) (cos x))
14.0ms
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
27.0ms
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
2.0s
(- (+ (/ (/ (sin x) (cos x)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))))) (/ (sin x) (cos x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (sin x) (cos x))
130.0ms
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
111.0ms
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
898.0ms
(- (+ (/ (/ (sin x) (cos x)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))))) (/ (sin x) (cos x)))

simplify1.0s

Counts
499 → 499
Iterations
IterNodes
12579
0537

prune8.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 17.0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sin x) (cos eps)) (/ (/ 1 (cos x)) (/ 1 (sin eps))))
0.3b
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
0.3b
(/ (/ 1 (cos x)) (/ 1 (sin eps)))
3.5b
(- (+ (/ (/ (sin x) (cos x)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps))))) (/ (/ (sin eps) (cos eps)) (- 1 (* (/ (sin x) (cos eps)) (/ (/ 1 (cos x)) (/ 1 (sin eps))))))) (/ (sin x) (cos x)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
1313×times-frac
671×add-sqr-sqrt
616×*-un-lft-identity
586×add-cube-cbrt
189×add-exp-log
174×associate-*r*
121×div-exp
86×div-inv
69×add-cbrt-cube
37×cbrt-undiv
34×prod-exp
26×associate-/r* associate-/l*
24×rec-exp 1-exp
20×unswap-sqr
13×associate-*l*
10×cbrt-unprod
9×add-log-exp
6×pow1
5×distribute-lft-out--
4×insert-posit16
3×associate-/r/ frac-sub distribute-lft-out
2×clear-num frac-2neg diff-log difference-of-squares associate-/l/
1×frac-times sum-log sub-neg flip3-+ flip3-- pow-prod-down associate-*l/ frac-add associate--l+ associate-*r/ *-commutative flip-+ flip--
Counts
4 → 732
Calls
4 calls:
34.0ms
(* (/ (sin x) (cos eps)) (/ (/ 1 (cos x)) (/ 1 (sin eps))))
14.0ms
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
12.0ms
(/ (/ 1 (cos x)) (/ 1 (sin eps)))
1.3s
(- (+ (/ (/ (sin x) (cos x)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps))))) (/ (/ (sin eps) (cos eps)) (- 1 (* (/ (sin x) (cos eps)) (/ (/ 1 (cos x)) (/ 1 (sin eps))))))) (/ (sin x) (cos x)))

series761.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (/ (sin x) (cos eps)) (/ (/ 1 (cos x)) (/ 1 (sin eps))))
132.0ms
(/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps)))
43.0ms
(/ (/ 1 (cos x)) (/ 1 (sin eps)))
440.0ms
(- (+ (/ (/ (sin x) (cos x)) (- 1 (/ (/ (sin x) (cos x)) (/ (cos eps) (sin eps))))) (/ (/ (sin eps) (cos eps)) (- 1 (* (/ (sin x) (cos eps)) (/ (/ 1 (cos x)) (/ 1 (sin eps))))))) (/ (sin x) (cos x)))

simplify3.1s

Counts
744 → 744
Iterations
IterNodes
15763
01122

prune9.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.9b

regimes121.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
219
119
016

end0.0ms

sample9.4s

Algorithm
intervals
Results
4.6s3252×body1280valid
1.8s1845×body640valid
1.5s643×body2560valid
804.0ms781×body320valid
371.0ms344×body160valid
198.0ms1135×body80valid