Details

Time bar (total: 26.7s)

sample433.0ms

Algorithm
intervals
Results
229.0ms120×body1280valid
100.0ms59×body640valid
62.0ms20×body2560valid
11.0ms13×body320valid
9.0ms14×body160valid
7.0ms30×body80valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (tan (+ x eps)) (tan x))
3.0b
(tan (+ x eps))

rewrite30.0ms

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:
24.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series235.0ms

Counts
2 → 6
Calls
2 calls:
144.0ms
(- (tan (+ x eps)) (tan x))
91.0ms
(tan (+ x eps))

simplify1.6s

Counts
33 → 33
Iterations
IterNodes
done2017
52017
41821
3719
2300
1139
070

prune196.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.4b

localize29.0ms

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))
0.3b
(* (tan x) (tan eps))
3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite191.0ms

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:
46.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms
(+ (tan x) (tan eps))
26.0ms
(* (tan x) (tan eps))
101.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
311.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
138.0ms
(+ (tan x) (tan eps))
146.0ms
(* (tan x) (tan eps))
473.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts
102 → 102
Iterations
IterNodes
done2000
32000
21148
1405
0174

prune615.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan eps))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
27.0b
(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
229×tan-quot
147×frac-times
87×associate-*l/
75×associate-*r/
63×cbrt-div
45×pow1
18×add-cbrt-cube pow-prod-down add-exp-log
13×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×*-un-lft-identity
6×add-cube-cbrt add-log-exp
4×associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16
2×pow-plus *-commutative difference-of-squares
1×cbrt-prod pow2 sub-neg times-frac flip3-- pow1/3 diff-log swap-sqr pow3 frac-sub rem-cbrt-cube flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 163
Calls
4 calls:
15.0ms
(* (tan x) (tan eps))
70.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
61.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
196.0ms
(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (tan x) (tan eps))
114.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
391.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
107.0ms
(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

simplify829.0ms

Counts
175 → 175
Iterations
IterNodes
done2008
22008
1857
0360

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize130.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.5b
(cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))
3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps)))) (cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))))) (tan x))
27.0b
(cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
43×pow1
17×pow-prod-down
16×add-cbrt-cube add-exp-log
11×associate-*l/
10×cbrt-div
9×add-sqr-sqrt tan-quot associate-*r/
8×prod-exp cos-mult cbrt-unprod
7×frac-times
6×*-un-lft-identity add-log-exp
4×pow-sqr pow-prod-up add-cube-cbrt insert-posit16 sin-mult
2×cbrt-prod pow-plus pow1/3 difference-of-squares
1×pow2 sub-neg times-frac flip3-- diff-log swap-sqr associate-*r* associate-*l* *-commutative frac-sub flip-- distribute-lft-out--
Counts
4 → 85
Calls
4 calls:
51.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
47.0ms
(cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))
1.3s
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps)))) (cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))))) (tan x))
202.0ms
(cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps))))

series1.5s

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
156.0ms
(cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))
958.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps)))) (cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))))) (tan x))
300.0ms
(cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps))))

simplify1.3s

Counts
97 → 97
Iterations
IterNodes
done2004
32004
21896
1522
0203

prune777.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.5b

regimes214.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify14.0ms

Iterations
IterNodes
done33
133
024

end0.0ms

sample12.3s

Algorithm
intervals
Results
6.5s3313×body1280valid
2.5s1822×body640valid
2.0s656×body2560valid
676.0ms769×body320valid
248.0ms1071×body80valid
196.0ms369×body160valid