Details

Time bar (total: 1.2m)

sample364.0ms

Algorithm
intervals
Results
112.0ms45×body640valid
70.0ms41×body1280valid
37.0ms143×body80valid
20.0ms23×body320valid
2.0ms4×body160valid

simplify99.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
98.0ms
(/ (- 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

localize29.0ms

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)))

rewrite55.0ms

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
19.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))
13.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(- 1 (* (tan x) (tan x)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
63.0ms
(* (tan x) (tan x))
59.0ms
(- 1 (* (tan x) (tan x)))
52.0ms
(* (tan x) (tan x))

simplify6.5s

Counts
111 → 126
Calls
111 calls:
Slowest
648.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
595.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
535.0ms
(/ (* (* (- 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)))))
499.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
349.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
204×*-un-lft-identity times-frac
156×add-sqr-sqrt
94×add-cube-cbrt
40×difference-of-squares
30×associate-/r*
25×distribute-lft-out
20×distribute-lft-out--
13×add-cbrt-cube add-exp-log associate-/r/
11×pow1
7×flip3-- div-inv flip-- associate-/l*
6×add-log-exp
4×cbrt-undiv div-exp tan-quot insert-posit16 associate-/l/
3×swap-sqr associate-*r* associate-*l*
2×clear-num frac-2neg flip3-+ flip-+
1×pow2 frac-times sub-neg pow-plus diff-log pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
4 → 231
Calls
4 calls:
Slowest
53.0ms
(/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x)))
41.0ms
(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
13.0ms
(* (tan x) (tan x))
4.0ms
(- 1 (tan x))

series256.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
61.0ms
(/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x)))
41.0ms
(* (tan x) (tan x))
22.0ms
(- 1 (tan x))

simplify28.6s

Counts
318 → 243
Calls
318 calls:
Slowest
767.0ms
(/ (* (cbrt (+ 1 (tan x))) (cbrt (+ 1 (tan x)))) (/ (* (cbrt (+ 1 (* (tan x) (tan x)))) (cbrt (+ 1 (* (tan x) (tan x))))) (+ 1 (sqrt (tan x)))))
649.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
588.0ms
(/ (* (* (+ 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (+ 1 (* (tan x) (tan x)))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
582.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
439.0ms
(+ (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×*-un-lft-identity
23×add-cube-cbrt
21×times-frac
15×add-cbrt-cube add-exp-log
13×pow1
8×difference-of-squares
7×associate-/l*
6×associate-/r* associate-*r* associate-*l* tan-quot
4×insert-posit16 distribute-lft-out-- add-log-exp
3×cbrt-undiv swap-sqr div-exp prod-exp associate-*r/ cbrt-unprod associate-/l/
2×clear-num frac-2neg pow-prod-down associate-/r/ *-commutative div-inv unswap-sqr
1×pow2 frac-times flip3-+ pow-plus flip3-- div-sub associate-*l/ pow-sqr pow-prod-up flip-+ flip--
Counts
4 → 117
Calls
4 calls:
Slowest
26.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
20.0ms
(* (tan x) (tan x))
15.0ms
(/ (* (sin x) (tan x)) (cos x))
11.0ms
(* (sin x) (tan x))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
83.0ms
(/ (* (sin x) (tan x)) (cos x))
54.0ms
(* (sin x) (tan x))
34.0ms
(* (tan x) (tan x))

simplify8.7s

Counts
113 → 129
Calls
113 calls:
Slowest
588.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
582.0ms
(- (pow 1 3) (pow (/ (* (sin x) (tan x)) (cos x)) 3))
538.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
453.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
310.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
47×add-sqr-sqrt
26×add-cube-cbrt
24×times-frac
20×pow1
12×add-cbrt-cube add-exp-log
10×difference-of-squares
9×associate-*r* associate-*l*
7×distribute-lft-out
6×swap-sqr associate-/l*
5×distribute-lft-out--
4×associate-/r* insert-posit16 add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×pow2 pow-plus associate-/r/ pow-sqr pow-prod-up associate-/l/
1×cbrt-undiv sqr-cos clear-num frac-2neg flip3-+ flip3-- div-sub div-exp tan-quot associate-*r/ cos-mult flip-+ sqr-sin div-inv flip-- sin-mult
Counts
4 → 128
Calls
4 calls:
Slowest
47.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x)))))
24.0ms
(* (sin x) (tan x))
23.0ms
(* (sin x) (sin x))
19.0ms
(* (cos x) (cos x))

series316.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x)))))
83.0ms
(* (sin x) (tan x))
29.0ms
(* (cos x) (cos x))
28.0ms
(* (sin x) (sin x))

simplify11.4s

Counts
132 → 140
Calls
132 calls:
Slowest
734.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
661.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
569.0ms
(- (pow 1 3) (pow (/ (* (sin x) (tan x)) (cos x)) 3))
457.0ms
(- (log (- 1 (/ (* (sin x) (tan x)) (cos x)))) (log (+ 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x))))))
424.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (/ (* (sin x) (sin x)) (* (cos x) (cos x)))))

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes250.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.5s1506×body1280valid
1.8s1300×body640valid
990.0ms4256×body80valid
542.0ms630×body320valid
130.0ms308×body160valid