Details

Time bar (total: 30.7s)

sample399.0ms

Algorithm
intervals
Results
173.0ms103×body1280valid
116.0ms16×body2560valid
55.0ms50×body640valid
26.0ms34×body320valid
9.0ms41×body80valid
6.0ms12×body160valid

simplify11.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize14.0ms

Local error

Found 2 expressions with local error:

2.6b
(tan (+ x eps))
1.9b
(- (tan (+ x eps)) (tan x))

rewrite28.0ms

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:
Slowest
22.0ms
(- (tan (+ x eps)) (tan x))
5.0ms
(tan (+ x eps))

series185.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
115.0ms
(- (tan (+ x eps)) (tan x))
69.0ms
(tan (+ x eps))

simplify1.2s

Counts
33 → 33

prune343.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.5b

localize48.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite95.0ms

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:
Slowest
50.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
22.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms
(* (tan x) (tan eps))
7.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
516.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
311.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
137.0ms
(+ (tan x) (tan eps))
118.0ms
(* (tan x) (tan eps))

simplify1.4s

Counts
102 → 102

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.4b

localize31.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
0.2b
(* (sin x) (tan eps))
0.2b
(/ (* (sin x) (tan eps)) (cos x))
0.1b
(+ (tan x) (tan eps))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×*-un-lft-identity
11×add-cbrt-cube add-exp-log
8×add-cube-cbrt add-log-exp
6×pow1
5×tan-quot
4×times-frac insert-posit16
3×associate-/r* associate-*r* associate-*l*
2×cbrt-undiv div-exp prod-exp associate-*r/ cbrt-unprod difference-of-squares
1×+-commutative clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log pow-prod-down frac-add *-commutative frac-sub flip-+ div-inv flip-- distribute-lft-out associate-/l* distribute-lft-out-- unswap-sqr associate-/l/
Counts
4 → 74
Calls
4 calls:
Slowest
167.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
21.0ms
(* (sin x) (tan eps))
14.0ms
(/ (* (sin x) (tan eps)) (cos x))
7.0ms
(+ (tan x) (tan eps))

series919.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
509.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
163.0ms
(/ (* (sin x) (tan eps)) (cos x))
139.0ms
(+ (tan x) (tan eps))
108.0ms
(* (sin x) (tan eps))

simplify1.9s

Counts
86 → 86

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.3b

localize73.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
73×tan-quot
37×frac-times
35×pow-prod-down
30×add-cbrt-cube add-exp-log
25×associate-*r/
24×associate-*l/
17×prod-exp cbrt-unprod
8×add-sqr-sqrt pow-sqr pow-prod-up
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×associate-*r* associate-*l* frac-sub
4×pow-plus insert-posit16
3×*-commutative
2×pow2 flip3-+ swap-sqr associate--l+ flip-+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log flip-- unswap-sqr
Counts
4 → 142
Calls
4 calls:
Slowest
105.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
85.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
81.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
19.0ms
(* (tan x) (tan eps))

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
2.0s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
160.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
156.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
135.0ms
(* (tan x) (tan eps))

simplify1.9s

Counts
154 → 154

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.3b

regimes292.0ms

Accuracy

90.6% (0.7b remaining)

Error of 14.9b against oracle of 14.1b and baseline of 21.7b

bsearch477.0ms

end0.0ms

sample12.9s

Algorithm
intervals
Results
6.7s3352×body1280valid
2.7s1845×body640valid
1.9s650×body2560valid
1.0s764×body320valid
214.0ms1035×body80valid
163.0ms354×body160valid