Details

Time bar (total: 29.5s)

sample295.0ms

Algorithm
intervals
Results
165.0ms110×body1280valid
61.0ms22×body2560valid
32.0ms50×body640valid
12.0ms30×body320valid
4.0ms16×body160valid
4.0ms28×body80valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize25.0ms

Local error

Found 2 expressions with local error:

1.7b
(- (tan (+ x eps)) (tan x))
3.2b
(tan (+ x eps))

rewrite34.0ms

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
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 25
Calls
2 calls:
23.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series587.0ms

Counts
2 → 6
Calls
2 calls:
491.0ms
(- (tan (+ x eps)) (tan x))
96.0ms
(tan (+ x eps))

simplify1.8s

Counts
31 → 31
Iterations
IterNodes
done5001
41748
3709
2298
1137
068

prune209.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.6b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite146.0ms

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×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 → 86
Calls
4 calls:
22.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
10.0ms
(+ (tan x) (tan eps))
16.0ms
(* (tan x) (tan eps))
95.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
295.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
167.0ms
(+ (tan x) (tan eps))
137.0ms
(* (tan x) (tan eps))
472.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.9s

Counts
98 → 98
Iterations
IterNodes
done5045
34214
21148
1401
0170

prune565.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.3b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
36×times-frac
33×*-un-lft-identity
26×associate-*r*
23×add-cbrt-cube add-exp-log
22×add-cube-cbrt
8×pow1
6×cbrt-undiv div-exp associate-*l* prod-exp cbrt-unprod add-log-exp difference-of-squares
4×distribute-lft-out-- unswap-sqr
3×associate-/r* associate-*r/ div-inv
2×pow-prod-down *-commutative
1×clear-num sub-neg frac-2neg flip3-- diff-log frac-sub flip-- associate-/l* associate-/l/
Counts
4 → 110
Calls
4 calls:
25.0ms
(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
28.0ms
(* (sin x) (/ (sin eps) (cos eps)))
30.0ms
(* (sin x) (/ (sin eps) (cos eps)))
219.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series758.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
148.0ms
(* (sin x) (/ (sin eps) (cos eps)))
107.0ms
(* (sin x) (/ (sin eps) (cos eps)))
363.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify1.7s

Counts
122 → 122
Iterations
IterNodes
done5001
21612
1484
0186

prune976.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.3b

localize137.0ms

Local error

Found 4 expressions with local error:

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

rewrite447.0ms

Algorithm
rewrite-expression-head
Rules
684×times-frac
526×*-un-lft-identity
501×add-sqr-sqrt
292×add-cube-cbrt
123×swap-sqr
110×associate-*r*
105×difference-of-squares
100×associate-*l*
78×distribute-lft-out--
57×add-cbrt-cube add-exp-log
37×div-inv
23×cbrt-undiv div-exp
20×pow1
15×prod-exp cbrt-unprod unswap-sqr
9×associate-*r/ frac-sub
8×frac-times associate-*l/ associate-/r/
6×add-log-exp
5×flip3-- flip--
3×pow-prod-down *-commutative
2×pow2 pow-plus pow-sqr pow-prod-up
1×sub-neg diff-log
Counts
4 → 442
Calls
4 calls:
30.0ms
(* (sin x) (/ (sin eps) (cos eps)))
28.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
279.0ms
(* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))))
46.0ms
(- (* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

series949.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (sin x) (/ (sin eps) (cos eps)))
90.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
289.0ms
(* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))))
434.0ms
(- (* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

simplify2.8s

Counts
454 → 454
Iterations
IterNodes
done5001
12732
0712

prune3.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.3b

regimes236.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done26
126
021

end0.0ms

sample9.9s

Algorithm
intervals
Results
4.7s3309×body1280valid
2.1s655×body2560valid
1.4s1843×body640valid
839.0ms1098×body80valid
507.0ms775×body320valid
95.0ms320×body160valid