Details

Time bar (total: 1.1m)

sample344.0ms

Algorithm
intervals
Results
68.0ms41×body1280valid
52.0ms45×body640valid
36.0ms143×body80valid
18.0ms23×body320valid
2.0ms4×body160valid

simplify78.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
78.0ms
(/ (- 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

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)))

rewrite53.0ms

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
Counts
4 → 128
Calls
4 calls:
Slowest
16.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
14.0ms
(* (tan x) (tan x))
6.0ms
(- 1 (* (tan x) (tan x)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
61.0ms
(- 1 (* (tan x) (tan x)))
56.0ms
(* (tan x) (tan x))
54.0ms
(* (tan x) (tan x))

simplify6.2s

Counts
119 → 140
Calls
119 calls:
Slowest
659.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
514.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
493.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
376.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
361.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
211×*-un-lft-identity
204×times-frac
163×add-sqr-sqrt
101×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
9×prod-diff
7×flip3-- div-inv flip-- associate-/l*
6×add-log-exp
4×expm1-log1p-u cbrt-undiv div-exp tan-quot insert-posit16 log1p-expm1-u associate-/l/
3×fma-neg 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 → 251
Calls
4 calls:
Slowest
50.0ms
(/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x)))
33.0ms
(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
20.0ms
(* (tan x) (tan x))
8.0ms
(- 1 (tan x))

series312.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
90.0ms
(/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x)))
42.0ms
(* (tan x) (tan x))
39.0ms
(- 1 (tan x))

simplify30.2s

Counts
338 → 263
Calls
338 calls:
Slowest
723.0ms
(/ (* (* (+ 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (+ 1 (* (tan x) (tan x)))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
539.0ms
(/ (sqrt (+ 1 (tan x))) (/ (+ 1 (* (tan x) (tan x))) (- (pow 1 3) (pow (tan x) 3))))
400.0ms
(/ (* (cbrt (+ 1 (tan x))) (cbrt (+ 1 (tan x)))) (/ (* (cbrt (+ 1 (* (tan x) (tan x)))) (cbrt (+ 1 (* (tan x) (tan x))))) (+ 1 (sqrt (tan x)))))
395.0ms
(/ (* (cbrt (+ 1 (tan x))) (cbrt (+ 1 (tan x)))) (/ (* (cbrt (+ 1 (* (tan x) (tan x)))) (cbrt (+ 1 (* (tan x) (tan x))))) (+ (sqrt 1) (sqrt (tan x)))))
394.0ms
(+ (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune2.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
30×*-un-lft-identity
28×add-cube-cbrt
21×pow1 associate-*r* add-exp-log
20×times-frac
15×add-cbrt-cube
11×associate-*l*
8×tan-quot
6×swap-sqr prod-exp
5×unswap-sqr
4×expm1-log1p-u frac-times div-exp associate-*l/ associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* pow-prod-down associate-*r/ *-commutative associate-/l*
2×pow2 cbrt-undiv rec-exp flip3-+ pow-plus flip3-- 1-exp pow-sqr pow-prod-up flip-+ div-inv flip-- difference-of-squares
1×clear-num frac-2neg un-div-inv pow-flip inv-pow
Counts
4 → 145
Calls
4 calls:
Slowest
35.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
34.0ms
(* (tan x) (tan x))
17.0ms
(* (tan x) (tan x))
7.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
75.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))
51.0ms
(* (tan x) (tan x))
49.0ms
(* (tan x) (tan x))

simplify8.6s

Counts
131 → 157
Calls
131 calls:
Slowest
855.0ms
(* (* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x)))) (* (* (/ 1 (+ 1 (* (tan x) (tan x)))) (/ 1 (+ 1 (* (tan x) (tan x))))) (/ 1 (+ 1 (* (tan x) (tan x))))))
559.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
551.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
461.0ms
(* (- (pow 1 3) (pow (* (tan x) (tan x)) 3)) 1)
454.0ms
(* (+ (* 1 1) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))) (+ 1 (* (tan x) (tan x))))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
3×cbrt-undiv swap-sqr div-exp associate-*l/ prod-exp 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-*r/ pow-sqr pow-prod-up flip-+ flip--
Counts
4 → 125
Calls
4 calls:
Slowest
66.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
22.0ms
(* (tan x) (tan x))
20.0ms
(* (tan x) (sin x))
16.0ms
(/ (* (tan x) (sin x)) (cos x))

series378.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
113.0ms
(/ (* (tan x) (sin x)) (cos x))
77.0ms
(* (tan x) (sin x))
47.0ms
(* (tan x) (tan x))

simplify8.6s

Counts
113 → 137
Calls
113 calls:
Slowest
597.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
560.0ms
(- (pow 1 3) (pow (/ (* (tan x) (sin x)) (cos x)) 3))
427.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
334.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))
283.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes196.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.6s1506×body1280valid
1.7s1300×body640valid
971.0ms4256×body80valid
416.0ms630×body320valid
189.0ms308×body160valid