Details

Time bar (total: 1.2m)

sample360.0ms

Algorithm
intervals
Results
164.0ms48×body1280valid
68.0ms39×body640valid
33.0ms136×body80valid
15.0ms21×body320valid
5.0ms12×body160valid

simplify229.0ms

Calls
1 calls:
Slowest
228.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×pow1
10×add-cbrt-cube add-exp-log
9×times-frac
8×tan-quot
6×associate-*r* associate-*l*
4×insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative pow-prod-up cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ div-sub div-exp flip-+ div-inv
Calls
4 calls:
Slowest
13.0ms
(* (tan x) (tan x))
10.0ms
(* (tan x) (tan x))
9.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
3.0ms
(- 1 (* (tan x) (tan x)))

series266.0ms

Calls
4 calls:
Slowest
87.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
86.0ms
(* (tan x) (tan x))
59.0ms
(* (tan x) (tan x))
34.0ms
(- 1 (* (tan x) (tan x)))

simplify3.8s

Calls
72 calls:
Slowest
700.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
542.0ms
(/ (* (* (- 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)))))
468.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
394.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
115.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune976.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube add-exp-log
26×associate-*r* associate-*l*
14×pow1
9×cbrt-undiv div-exp
8×prod-exp cbrt-unprod
5×div-inv
4×insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ associate-*r/ associate-/r/ *-commutative pow-prod-up flip-- associate-/l/
1×clear-num sub-neg frac-2neg flip3-+ div-sub flip-+
Calls
4 calls:
Slowest
15.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
14.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
9.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
3.0ms
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

series302.0ms

Calls
4 calls:
Slowest
132.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
70.0ms
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
51.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
48.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify8.2s

Calls
124 calls:
Slowest
444.0ms
(- (* 1 1) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
416.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
348.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
346.0ms
(- (pow 1 3) (pow (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) 3))
332.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

9.1b
(cbrt (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
158×add-cbrt-cube add-exp-log
148×frac-times
88×associate-*l/
76×associate-*r/
73×prod-exp cbrt-unprod
71×pow1
63×cbrt-div
48×cbrt-undiv div-exp
36×times-frac
32×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×associate-*r* associate-*l*
25×pow-prod-up
20×pow-prod-down
14×pow-plus
11×pow2
4×insert-posit16 div-inv add-log-exp
3×*-commutative
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
125.0ms
(cbrt (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
39.0ms
(* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
18.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
11.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series266.0ms

Calls
4 calls:
Slowest
83.0ms
(* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
62.0ms
(cbrt (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
61.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
59.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify43.8s

Calls
276 calls:
Slowest
909.0ms
(* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
883.0ms
(* (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)))))
848.0ms
(* (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)))) (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
775.0ms
(* (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)))) (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)))))
627.0ms
(cbrt (* (* (* (sin x) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (sin x))))

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (* (tan x) (tan x)) 3)
0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
77×pow1
44×tan-quot
26×pow-prod-up
23×add-cbrt-cube add-exp-log
21×pow-prod-down
20×frac-times
15×pow-plus
14×associate-*l/ associate-*r/
12×pow2
11×prod-exp cbrt-unprod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
5×pow-pow
4×insert-posit16 add-log-exp
3×cube-div *-commutative
2×pow-exp rem-cube-cbrt
1×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod
Calls
4 calls:
Slowest
44.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
8.0ms
(* (tan x) (tan x))
8.0ms
(pow (* (tan x) (tan x)) 3)
6.0ms
(* (tan x) (tan x))

series228.0ms

Calls
4 calls:
Slowest
77.0ms
(pow (* (tan x) (tan x)) 3)
76.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
39.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))

simplify1.9s

Calls
131 calls:
Slowest
143.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
117.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
113.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
93.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
73.0ms
(pow (* (tan x) (sin x)) 3)

prune1.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes325.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch2.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.0s1447×body1280valid
1.7s1343×body640valid
787.0ms4279×body80valid
428.0ms630×body320valid
116.0ms301×body160valid