Details

Time bar (total: 5.1m)

sample697.0ms

Algorithm
intervals
Results
481.0ms143×body80valid
63.0ms44×body1280valid
41.0ms43×body640valid
11.0ms15×body320valid
5.0ms11×body160valid

simplify107.0ms

Calls
1 calls:
Slowest
106.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
161×*-un-lft-identity
143×add-sqr-sqrt
75×times-frac
70×difference-of-squares
34×add-cube-cbrt
32×distribute-lft-out
29×associate-*l*
20×swap-sqr
18×pow1
16×*-commutative unswap-sqr
15×associate-/l*
14×distribute-lft-out--
10×add-cbrt-cube add-exp-log
8×tan-quot
6×associate-*r* add-log-exp
5×associate-/r*
4×insert-posit16
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr pow-prod-up cbrt-unprod flip-- 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
94.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
23.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))
12.0ms
(- 1 (* (tan x) (tan x)))

series291.0ms

Calls
4 calls:
Slowest
143.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
66.0ms
(* (tan x) (tan x))
45.0ms
(- 1 (* (tan x) (tan x)))
36.0ms
(* (tan x) (tan x))

simplify12.9s

Calls
259 calls:
Slowest
649.0ms
(/ (* (* (- 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)))))
647.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
609.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
447.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
345.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
627×*-un-lft-identity
543×times-frac
514×add-sqr-sqrt
220×difference-of-squares
180×add-cube-cbrt
124×distribute-lft-out
96×associate-/r*
90×associate-*l*
50×swap-sqr
46×*-commutative unswap-sqr
44×distribute-lft-out--
33×associate-/r/
19×pow1 add-exp-log
13×add-cbrt-cube
11×associate-/l*
8×tan-quot
7×div-exp
6×associate-*r* add-log-exp
5×flip3-- div-inv flip--
4×insert-posit16 remove-double-div
3×cbrt-undiv clear-num
2×pow2 frac-times rec-exp frac-2neg pow-plus 1-exp pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr pow-prod-up cbrt-unprod associate-/l/
1×sub-neg flip3-+ diff-log flip-+ pow-flip inv-pow
Calls
4 calls:
Slowest
109.0ms
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
26.0ms
(* (tan x) (tan x))
17.0ms
(- 1 (* (tan x) (tan x)))
13.0ms
(* (tan x) (tan x))

series291.0ms

Calls
4 calls:
Slowest
138.0ms
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
59.0ms
(- 1 (* (tan x) (tan x)))
48.0ms
(* (tan x) (tan x))
45.0ms
(* (tan x) (tan x))

simplify1.1m

Calls
690 calls:
Slowest
652.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
576.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
553.0ms
(/ (sqrt 1) (/ (+ 1 (* (tan x) (tan x))) (- (sqrt 1) (tan x))))
478.0ms
(* (- 1 (* (tan x) (tan x))) (+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))))
410.0ms
(/ (* (* 1 1) 1) (* (* (/ (+ 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))))))

prune4.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize1.0ms

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))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
161×*-un-lft-identity
143×add-sqr-sqrt
75×times-frac
70×difference-of-squares
34×add-cube-cbrt
32×distribute-lft-out
29×associate-*l*
20×swap-sqr
18×pow1
16×*-commutative unswap-sqr
15×associate-/l*
14×distribute-lft-out--
10×add-cbrt-cube add-exp-log
8×tan-quot
6×associate-*r* add-log-exp
5×associate-/r*
4×insert-posit16
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr pow-prod-up cbrt-unprod flip-- 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
78.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
27.0ms
(* (tan x) (tan x))
20.0ms
(- 1 (* (tan x) (tan x)))
14.0ms
(* (tan x) (tan x))

series262.0ms

Calls
4 calls:
Slowest
127.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
61.0ms
(* (tan x) (tan x))
39.0ms
(- 1 (* (tan x) (tan x)))
35.0ms
(* (tan x) (tan x))

simplify13.3s

Calls
259 calls:
Slowest
717.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
709.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
644.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
539.0ms
(/ (* (* (- 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)))))
489.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

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))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
444×*-un-lft-identity
286×frac-sub
243×associate-/l*
225×add-sqr-sqrt
213×associate-/r*
140×add-cube-cbrt
116×distribute-lft-out
111×associate-*l*
74×times-frac
56×tan-quot
45×swap-sqr
42×associate-*r*
39×frac-2neg
37×clear-num
33×associate-/l/
25×pow1
24×distribute-lft-out--
19×sub-div
18×difference-of-squares
17×*-commutative unswap-sqr
14×frac-times associate-*l/ associate-*r/
10×add-cbrt-cube add-exp-log
7×distribute-rgt-out-- div-inv
6×add-log-exp
4×associate-/r/ insert-posit16
3×pow2 pow-plus pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod
2×flip3-+ flip-+
1×sub-neg flip3-- diff-log flip--
Calls
4 calls:
Slowest
181.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
29.0ms
(* (tan x) (tan x))
27.0ms
(* (tan x) (tan x))
21.0ms
(* (tan x) (tan x))

series285.0ms

Calls
4 calls:
Slowest
156.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
60.0ms
(* (tan x) (tan x))
36.0ms
(* (tan x) (tan x))
32.0ms
(* (tan x) (tan x))

simplify3.2m

Calls
794 calls:
Slowest
945.0ms
(* (/ (+ 1 (* (tan x) (tan x))) 1) (/ (+ 1 (* (tan x) (tan x))) (* (sqrt (tan x)) (sqrt (tan x)))))
892.0ms
(* (cbrt (+ 1 (* (tan x) (tan x)))) (/ (+ 1 (* (tan x) (tan x))) (* (sqrt (tan x)) (sqrt (tan x)))))
860.0ms
(* (+ 1 (* (tan x) (tan x))) (/ (+ 1 (* (tan x) (tan x))) (* (sqrt (tan x)) (sqrt (tan x)))))
855.0ms
(* (+ 1 (* (tan x) (tan x))) (/ (+ 1 (* (tan x) (tan x))) (* (sqrt (tan x)) (sqrt (tan x)))))
771.0ms
(- (* 1 (- (+ 1 (* (tan x) (tan x))))) (* (+ 1 (* (tan x) (tan x))) (- (* (tan x) (tan x)))))

prune4.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes238.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.3s1540×body1280valid
1.3s1256×body640valid
923.0ms4300×body80valid
913.0ms589×body320valid
173.0ms315×body160valid