Details

Time bar (total: 31.1s)

sample272.0ms

Algorithm
intervals
Results
120.0ms112×body1280valid
60.0ms25×body2560valid
33.0ms38×body80valid
28.0ms44×body640valid
12.0ms26×body320valid
3.0ms11×body160valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize25.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (tan (+ x eps)) (tan x))
3.7b
(tan (+ x eps))

rewrite38.0ms

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

series272.0ms

Counts
2 → 6
Calls
2 calls:
149.0ms
(- (tan (+ x eps)) (tan x))
123.0ms
(tan (+ x eps))

simplify1.7s

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

prune233.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.9b

localize41.0ms

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))
2.5b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite188.0ms

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:
12.0ms
(+ (tan x) (tan eps))
43.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
23.0ms
(* (tan x) (tan eps))
105.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
121.0ms
(+ (tan x) (tan eps))
309.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
111.0ms
(* (tan x) (tan eps))
509.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.7s

Counts
98 → 98
Iterations
IterNodes
done5083
34259
21147
1401
0170

prune754.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
0.2b
(/ (* (tan x) (sin eps)) (cos eps))
0.2b
(* (tan x) (sin eps))
2.5b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
42×add-sqr-sqrt
28×times-frac
20×add-cube-cbrt
13×add-cbrt-cube add-exp-log
12×difference-of-squares
9×associate-/r*
7×distribute-lft-out
6×pow1 distribute-lft-out-- add-log-exp
5×tan-quot associate-/l*
4×associate-/l/
3×cbrt-undiv div-exp associate-*r* associate-*l*
2×clear-num frac-2neg flip3-- associate-*l/ prod-exp associate-/r/ cbrt-unprod div-inv flip--
1×sub-neg flip3-+ diff-log pow-prod-down frac-add *-commutative frac-sub flip-+ unswap-sqr
Counts
4 → 108
Calls
4 calls:
34.0ms
(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
23.0ms
(/ (* (tan x) (sin eps)) (cos eps))
13.0ms
(* (tan x) (sin eps))
136.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
298.0ms
(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
148.0ms
(/ (* (tan x) (sin eps)) (cos eps))
124.0ms
(* (tan x) (sin eps))
531.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify1.5s

Counts
120 → 120
Iterations
IterNodes
done5001
21463
1504
0217

prune922.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.8b

localize150.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (tan x) (/ (cos eps) (sin eps)))
0.3b
(/ (tan x) (/ (cos eps) (sin eps)))
0.3b
(/ (tan x) (/ (cos eps) (sin eps)))
2.5b
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (/ (tan x) (/ (cos eps) (sin eps))) (/ (tan x) (/ (cos eps) (sin eps)))) (/ (tan x) (/ (cos eps) (sin eps)))))) (+ (* 1 1) (+ (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))) (* 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
225×times-frac
130×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
39×associate-/r*
19×add-cbrt-cube add-exp-log
15×div-inv
9×cbrt-undiv div-exp associate-/l*
8×tan-quot
6×add-log-exp
5×frac-sub
4×pow1
3×clear-num frac-2neg associate-/r/ associate-/l/
2×frac-times flip3-+ associate--l+ associate-*r/ flip-+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log associate-*l/ flip--
Counts
4 → 232
Calls
4 calls:
18.0ms
(/ (tan x) (/ (cos eps) (sin eps)))
19.0ms
(/ (tan x) (/ (cos eps) (sin eps)))
17.0ms
(/ (tan x) (/ (cos eps) (sin eps)))
147.0ms
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (/ (tan x) (/ (cos eps) (sin eps))) (/ (tan x) (/ (cos eps) (sin eps)))) (/ (tan x) (/ (cos eps) (sin eps)))))) (+ (* 1 1) (+ (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))) (* 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

series3.0s

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (tan x) (/ (cos eps) (sin eps)))
158.0ms
(/ (tan x) (/ (cos eps) (sin eps)))
150.0ms
(/ (tan x) (/ (cos eps) (sin eps)))
2.6s
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (/ (tan x) (/ (cos eps) (sin eps))) (/ (tan x) (/ (cos eps) (sin eps)))) (/ (tan x) (/ (cos eps) (sin eps)))))) (+ (* 1 1) (+ (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))) (* 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))

simplify2.8s

Counts
244 → 244
Iterations
IterNodes
done5031
23322
1826
0284

prune2.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.7b

regimes420.0ms

Accuracy

92.4% (0.6b remaining)

Error of 14.4b against oracle of 13.8b and baseline of 21.8b

bsearch382.0ms

Steps
ItersRangePoint
10
5.309240381750136e-51
1.1823000763036376e-39
8.988728992921953e-40
10
-1.427556205083161e-53
-2.3741323209942624e-63
-1.4110318888423867e-53

simplify14.0ms

Iterations
IterNodes
done48
148
032

end0.0ms

sample10.5s

Algorithm
intervals
Results
5.3s3312×body1280valid
2.2s671×body2560valid
1.5s1809×body640valid
554.0ms1074×body80valid
457.0ms798×body320valid
165.0ms336×body160valid