Details

Time bar (total: 58.8s)

sample175.0ms

Algorithm
intervals
Results
52.0ms138×body80valid
39.0ms42×body1280valid
33.0ms51×body640valid
7.0ms15×body320valid
3.0ms10×body160valid

simplify85.0ms

Calls
1 calls:
Slowest
85.0ms
(/ (- 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

localize16.0ms

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
24×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×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg prod-diff
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
Calls
4 calls:
Slowest
20.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))
13.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(- 1 (* (tan x) (tan x)))

series328.0ms

Calls
4 calls:
Slowest
131.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
70.0ms
(* (tan x) (tan x))
68.0ms
(* (tan x) (tan x))
59.0ms
(- 1 (* (tan x) (tan x)))

simplify5.6s

Calls
119 calls:
Slowest
545.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
445.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
385.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
345.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
325.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
39×*-un-lft-identity
31×add-cube-cbrt
27×prod-diff
13×pow1 add-cbrt-cube add-exp-log
11×distribute-rgt-in distribute-lft-in
9×frac-times associate-*r*
8×associate-/l/
7×flip3-+ flip3-- associate-*l* flip-+ flip--
6×add-log-exp
5×associate-*l/ associate-*r/
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* sub-neg times-frac fma-neg swap-sqr prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down associate-/r/ *-commutative distribute-lft-out-- unswap-sqr
1×pow2 clear-num frac-2neg pow-plus diff-log pow-sqr pow-prod-up div-inv distribute-lft-out associate-/l*
Calls
4 calls:
Slowest
43.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
41.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
13.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (tan x))

series255.0ms

Calls
4 calls:
Slowest
112.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
70.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
46.0ms
(* (tan x) (tan x))
26.0ms
(- 1 (tan x))

simplify22.3s

Calls
134 calls:
Slowest
1.0s
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
957.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
956.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
900.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
880.0ms
(* (+ (pow 1 3) (pow (tan x) 3)) (- (* 1 1) (* (tan x) (tan x))))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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))

rewrite176.0ms

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×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
Calls
4 calls:
Slowest
101.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
28.0ms
(* (tan x) (tan x))
28.0ms
(* (tan x) (tan x))
17.0ms
(* (tan x) (tan x))

series234.0ms

Calls
4 calls:
Slowest
69.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
63.0ms
(* (tan x) (tan x))
58.0ms
(* (tan x) (tan x))
44.0ms
(* (tan x) (tan x))

simplify5.1s

Calls
202 calls:
Slowest
455.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
350.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
312.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
285.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
264.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
26×add-cube-cbrt
21×prod-diff
13×pow1 add-cbrt-cube add-exp-log
12×times-frac
6×associate-*r* associate-*l* tan-quot add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×associate-/r* fma-neg swap-sqr associate-*l/ prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative difference-of-squares unswap-sqr
1×pow2 frac-times clear-num sub-neg frac-2neg pow-plus flip3-- diff-log associate-*r/ pow-sqr pow-prod-up flip-- associate-/l* distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
28.0ms
(* (tan x) (tan x))
21.0ms
(* (tan x) (sin x))
17.0ms
(/ (* (tan x) (sin x)) (cos x))
9.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))

series253.0ms

Calls
4 calls:
Slowest
85.0ms
(/ (* (tan x) (sin x)) (cos x))
63.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))
54.0ms
(* (tan x) (tan x))
51.0ms
(* (tan x) (sin x))

simplify11.4s

Calls
113 calls:
Slowest
591.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (/ (* (tan x) (sin x)) (cos x)) 1)))
344.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (/ 1 (cos x)) (* (tan x) (sin x)))))
300.0ms
(fma 1 1 (- (* (/ 1 (cos x)) (* (tan x) (sin x)))))
298.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
296.0ms
(fma (- (/ (sin x) (cbrt (cos x)))) (/ (tan x) (* (cbrt (cos x)) (cbrt (cos x)))) (* (/ (sin x) (cbrt (cos x))) (/ (tan x) (* (cbrt (cos x)) (cbrt (cos x))))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes344.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.2s1455×body1280valid
1.8s1278×body640valid
1.0s4347×body80valid
831.0ms610×body320valid
162.0ms310×body160valid