Details

Time bar (total: 28.7s)

sample200.0ms

Algorithm
intervals
Results
67.0ms49×body640valid
55.0ms53×body1280valid
18.0ms126×body80valid
9.0ms19×body320valid
3.0ms9×body160valid

simplify69.0ms

Calls
1 calls:
Slowest
69.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

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)))

rewrite20.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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
7.0ms
(* (tan x) (tan x))
5.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(* (tan x) (tan x))
1.0ms
(- 1 (* (tan x) (tan x)))

series171.0ms

Calls
4 calls:
Slowest
61.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
46.0ms
(* (tan x) (tan x))
38.0ms
(- 1 (* (tan x) (tan x)))
25.0ms
(* (tan x) (tan x))

simplify3.5s

Calls
72 calls:
Slowest
686.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
403.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
398.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
192.0ms
(/ (* (* (- 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)))))
101.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
76×pow1
44×tan-quot
26×pow-prod-up
22×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
10×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
Calls
4 calls:
Slowest
20.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))

series140.0ms

Calls
4 calls:
Slowest
41.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))
36.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
26.0ms
(* (tan x) (tan x))

simplify2.1s

Calls
132 calls:
Slowest
150.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
146.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
131.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
105.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
66.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
16×log-pow
15×pow1 exp-prod
10×add-cbrt-cube add-exp-log
8×tan-quot
6×associate-*r* associate-*l*
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/r* associate-/l*
2×pow2 frac-times flip3-+ pow-plus div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip-+ div-inv associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-- exp-diff div-exp rem-log-exp flip--
Calls
4 calls:
Slowest
13.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
7.0ms
(* (tan x) (tan x))
5.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(* (tan x) (tan x))

series239.0ms

Calls
4 calls:
Slowest
98.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
73.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
42.0ms
(* (tan x) (tan x))
26.0ms
(* (tan x) (tan x))

simplify4.8s

Calls
92 calls:
Slowest
368.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
357.0ms
(/ (- 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))
342.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
318.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
18×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×add-cbrt-cube add-exp-log
9×times-frac associate-*r* associate-*l*
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u add-log-exp
3×pow2 associate-/r* pow-plus pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod associate-/l*
2×associate-/r/ associate-/l/
1×frac-times cbrt-undiv sqr-cos clear-num frac-2neg flip3-+ flip3-- div-sub div-exp associate-*l/ associate-*r/ cos-mult flip-+ sqr-sin div-inv flip-- sin-mult
Calls
4 calls:
Slowest
11.0ms
(/ (- 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x)))) (+ 1 (* (tan x) (tan x))))
5.0ms
(* (tan x) (tan x))
4.0ms
(* (sin x) (sin x))
4.0ms
(* (cos x) (cos x))

series125.0ms

Calls
4 calls:
Slowest
66.0ms
(/ (- 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x)))) (+ 1 (* (tan x) (tan x))))
30.0ms
(* (tan x) (tan x))
18.0ms
(* (sin x) (sin x))
11.0ms
(* (cos x) (cos x))

simplify5.4s

Calls
83 calls:
Slowest
393.0ms
(/ (- 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x)))) (+ 1 (* (tan x) (tan x))))
354.0ms
(/ (- 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x)))) (cbrt (+ 1 (* (tan x) (tan x)))))
347.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
324.0ms
(/ (- 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x)))) (sqrt (+ 1 (* (tan x) (tan x)))))
318.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes274.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.3s1469×body1280valid
1.9s1238×body640valid
879.0ms4377×body80valid
532.0ms299×body160valid
452.0ms617×body320valid