Details

Time bar (total: 42.8s)

sample465.0ms

Algorithm
intervals
Results
88.0ms52×body640valid
64.0ms38×body1280valid
33.0ms138×body80valid
15.0ms20×body320valid
4.0ms8×body160valid

simplify144.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
143.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.1b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
27×*-un-lft-identity
22×add-cube-cbrt
18×pow1
15×times-frac
10×add-cbrt-cube add-exp-log difference-of-squares
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×associate-/l*
4×insert-posit16
3×associate-/r*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
4 → 114
Calls
4 calls:
Slowest
39.0ms
(* (tan x) (tan x))
25.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
25.0ms
(* (tan x) (tan x))
8.0ms
(- 1 (* (tan x) (tan x)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
78.0ms
(* (tan x) (tan x))
63.0ms
(- 1 (* (tan x) (tan x)))
50.0ms
(* (tan x) (tan x))

simplify7.4s

Counts
111 → 126
Calls
111 calls:
Slowest
1.1s
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
676.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
567.0ms
(/ (* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x)))) (* (* (+ 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (+ 1 (* (tan x) (tan x)))))
497.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
387.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune991.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.2b
(* (tan x) (sin x))
0.2b
(/ (* (tan x) (sin x)) (cos x))
0.1b
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×*-un-lft-identity
23×add-cube-cbrt
21×times-frac
15×add-cbrt-cube add-exp-log
13×pow1
8×difference-of-squares
7×associate-/l*
6×associate-/r* associate-*r* associate-*l* tan-quot
4×insert-posit16 distribute-lft-out-- add-log-exp
3×cbrt-undiv swap-sqr div-exp associate-*l/ prod-exp cbrt-unprod associate-/l/
2×clear-num frac-2neg pow-prod-down associate-/r/ *-commutative div-inv unswap-sqr
1×pow2 frac-times flip3-+ pow-plus flip3-- div-sub associate-*r/ pow-sqr pow-prod-up flip-+ flip--
Counts
4 → 117
Calls
4 calls:
Slowest
30.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
28.0ms
(/ (* (tan x) (sin x)) (cos x))
24.0ms
(* (tan x) (sin x))
20.0ms
(* (tan x) (tan x))

series343.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
86.0ms
(/ (* (tan x) (sin x)) (cos x))
58.0ms
(* (tan x) (tan x))
57.0ms
(* (tan x) (sin x))

simplify9.5s

Counts
113 → 129
Calls
113 calls:
Slowest
645.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
640.0ms
(- (pow 1 3) (pow (/ (* (tan x) (sin x)) (cos x)) 3))
593.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
471.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
353.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
136×pow1
44×tan-quot
39×pow-prod-up
26×pow-prod-down
25×pow-sqr
22×add-sqr-sqrt add-cbrt-cube add-exp-log
21×pow-plus
20×frac-times
16×pow2 *-un-lft-identity add-cube-cbrt
14×associate-*l/ associate-*r/
11×prod-exp cbrt-unprod
10×swap-sqr associate-*r* associate-*l*
4×*-commutative insert-posit16 add-log-exp unswap-sqr
Counts
4 → 166
Calls
4 calls:
Slowest
99.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
27.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series237.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
67.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
63.0ms
(* (tan x) (tan x))
57.0ms
(* (tan x) (tan x))
49.0ms
(* (tan x) (tan x))

simplify5.6s

Counts
202 → 178
Calls
202 calls:
Slowest
533.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
448.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
427.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
368.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
296.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
25×pow1
24×*-un-lft-identity
16×add-cube-cbrt
12×tan-quot
10×add-cbrt-cube add-exp-log
9×swap-sqr associate-*r* associate-*l*
8×times-frac
6×add-log-exp difference-of-squares
5×distribute-rgt-out-- div-inv
4×associate-/r/ insert-posit16
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
2×flip3-+ flip-+ distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 115
Calls
4 calls:
Slowest
46.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
27.0ms
(* (tan x) (tan x))
19.0ms
(* (tan x) (tan x))
13.0ms
(* (tan x) (tan x))

series317.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
61.0ms
(* (tan x) (tan x))
61.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))

simplify5.8s

Counts
116 → 127
Calls
116 calls:
Slowest
544.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
493.0ms
(- (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)) (/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))))
435.0ms
(- (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)) (/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))))
362.0ms
(- (* 1 (+ 1 (* (tan x) (tan x)))) (* (+ 1 (* (tan x) (tan x))) (* (tan x) (tan x))))
338.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes261.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.7s1477×body1280valid
1.4s1263×body640valid
1.4s4308×body80valid
523.0ms634×body320valid
183.0ms318×body160valid