Details

Time bar (total: 59.9s)

sample184.0ms

Algorithm
intervals
Results
44.0ms50×body1280valid
26.0ms39×body640valid
18.0ms143×body80valid
6.0ms14×body320valid
3.0ms10×body160valid

simplify92.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
91.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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
16.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
14.0ms
(* (tan x) (tan x))
7.0ms
(- 1 (* (tan x) (tan x)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
82.0ms
(* (tan x) (tan x))
41.0ms
(- 1 (* (tan x) (tan x)))
38.0ms
(* (tan x) (tan x))

simplify9.5s

Counts
153 → 126
Calls
153 calls:
Slowest
610.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
584.0ms
(/ (* (* (- 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)))))
578.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
500.0ms
(* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x))))
339.0ms
(* (* (/ (- 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)))))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))

rewrite159.0ms

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
94.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
26.0ms
(* (tan x) (tan x))
22.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series184.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
45.0ms
(* (tan x) (tan x))
41.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))

simplify7.8s

Counts
196 → 178
Calls
196 calls:
Slowest
529.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (* (tan x) (tan x)) (* (tan x) (tan x)))) (* (* (tan x) (tan x)) (* (tan x) (tan x))))
500.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
484.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
322.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
307.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.2b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.2b
(/ (sin x) (cos x))
0.2b
(/ (sin x) (cos x))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
100×add-sqr-sqrt
98×times-frac
76×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
18×pow1
10×cbrt-undiv div-exp div-inv
8×prod-exp cbrt-unprod unswap-sqr
6×associate-/r* associate-/l*
4×insert-posit16 add-log-exp
2×pow2 frac-times quot-tan clear-num frac-2neg pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 194
Calls
4 calls:
Slowest
37.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
28.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
16.0ms
(/ (sin x) (cos x))
16.0ms
(/ (sin x) (cos x))

series174.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
57.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
56.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
36.0ms
(/ (sin x) (cos x))
25.0ms
(/ (sin x) (cos x))

simplify15.9s

Counts
256 → 206
Calls
256 calls:
Slowest
474.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))
466.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
441.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))
409.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
372.0ms
(* (/ (sin x) (cos x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.2b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
39×*-un-lft-identity
32×add-cube-cbrt
30×times-frac
22×log-pow
21×exp-prod
19×pow1
14×difference-of-squares
10×add-cbrt-cube add-exp-log
8×tan-quot
6×swap-sqr associate-*r* associate-*l*
5×associate-/l*
4×associate-/r/ insert-posit16 add-log-exp
3×log-prod associate-/r*
2×pow2 frac-times flip3-+ pow-plus div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv unswap-sqr associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-- exp-diff div-exp rem-log-exp flip--
Counts
4 → 134
Calls
4 calls:
Slowest
28.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
26.0ms
(* (tan x) (tan x))
21.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
17.0ms
(* (tan x) (tan x))

series344.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
114.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
58.0ms
(* (tan x) (tan x))
48.0ms
(* (tan x) (tan x))

simplify12.6s

Counts
172 → 146
Calls
172 calls:
Slowest
997.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
672.0ms
(/ (* (* (- 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)))))
659.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
642.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
559.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes204.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.5s1517×body1280valid
1.3s1227×body640valid
951.0ms4317×body80valid
471.0ms605×body320valid
138.0ms334×body160valid