Details

Time bar (total: 48.9s)

sample358.0ms

Algorithm
intervals
Results
67.0ms48×body1280valid
43.0ms42×body640valid
33.0ms142×body80valid
14.0ms18×body320valid
2.0ms6×body160valid

simplify116.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
116.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

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
25.0ms
(* (tan x) (tan x))
23.0ms
(* (tan x) (tan x))
16.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(- 1 (* (tan x) (tan x)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
79.0ms
(* (tan x) (tan x))
56.0ms
(- 1 (* (tan x) (tan x)))
40.0ms
(* (tan x) (tan x))

simplify5.9s

Counts
119 → 140
Calls
119 calls:
Slowest
565.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
558.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
434.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
307.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
304.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite142.0ms

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
58.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
33.0ms
(* (tan x) (sin x))
32.0ms
(/ (* (tan x) (sin x)) (cos x))
18.0ms
(* (tan x) (tan x))

series345.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
86.0ms
(* (tan x) (sin x))
70.0ms
(/ (* (tan x) (sin x)) (cos x))
43.0ms
(* (tan x) (tan x))

simplify9.6s

Counts
113 → 137
Calls
113 calls:
Slowest
696.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
664.0ms
(- (pow 1 3) (pow (/ (* (tan x) (sin x)) (cos x)) 3))
555.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
514.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
362.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
29×add-sqr-sqrt
25×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube
19×associate-*r*
18×pow1 times-frac
14×prod-exp
8×cbrt-unprod
7×associate-*l* tan-quot
5×div-exp pow-prod-down associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* swap-sqr *-commutative associate-/l*
2×frac-times rec-exp 1-exp associate-*r/ associate-/r/ div-inv unswap-sqr associate-/l/
1×pow2 clear-num frac-2neg flip3-+ pow-plus flip3-- div-sub pow-sqr un-div-inv pow-prod-up flip-+ flip--
Counts
4 → 131
Calls
4 calls:
Slowest
73.0ms
(* (* (tan x) (sin x)) (/ 1 (cos x)))
33.0ms
(/ (- 1 (* (* (tan x) (sin x)) (/ 1 (cos x)))) (+ 1 (* (tan x) (tan x))))
30.0ms
(* (tan x) (tan x))
27.0ms
(* (tan x) (sin x))

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (- 1 (* (* (tan x) (sin x)) (/ 1 (cos x)))) (+ 1 (* (tan x) (tan x))))
103.0ms
(* (* (tan x) (sin x)) (/ 1 (cos x)))
61.0ms
(* (tan x) (tan x))
55.0ms
(* (tan x) (sin x))

simplify12.8s

Counts
111 → 143
Calls
111 calls:
Slowest
833.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x))) (* (* (/ 1 (cos x)) (/ 1 (cos x))) (/ 1 (cos x))))
707.0ms
(- (* 1 1) (* (* (* (tan x) (sin x)) (/ 1 (cos x))) (* (* (tan x) (sin x)) (/ 1 (cos x)))))
646.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
599.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
484.0ms
(/ (- 1 (* (* (tan x) (sin x)) (/ 1 (cos x)))) (+ 1 (* (tan x) (tan x))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))

rewrite160.0ms

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
Counts
4 → 174
Calls
4 calls:
Slowest
94.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
26.0ms
(* (tan x) (tan x))
21.0ms
(* (tan x) (tan x))
17.0ms
(* (tan x) (tan x))

series192.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
59.0ms
(* (tan x) (tan x))
54.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
42.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))

simplify5.2s

Counts
202 → 186
Calls
202 calls:
Slowest
411.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
385.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
329.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
283.0ms
(+ (* 6/5 (pow x 8)) (+ (pow x 4) (* 4/3 (pow x 6))))
263.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes265.0ms

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
2.6s1509×body1280valid
1.8s1284×body640valid
932.0ms4271×body80valid
545.0ms625×body320valid
129.0ms311×body160valid