Details

Time bar (total: 42.2s)

sample232.0ms

Algorithm
intervals
Results
58.0ms133×body80valid
48.0ms51×body1280valid
29.0ms44×body640valid
12.0ms22×body320valid
2.0ms6×body160valid

simplify103.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
103.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

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)))

rewrite68.0ms

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
24.0ms
(* (tan x) (tan x))
16.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
13.0ms
(* (tan x) (tan x))
11.0ms
(- 1 (* (tan x) (tan x)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
62.0ms
(* (tan x) (tan x))
58.0ms
(* (tan x) (tan x))
43.0ms
(- 1 (* (tan x) (tan x)))

simplify6.2s

Counts
119 → 140
Calls
119 calls:
Slowest
610.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
563.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
372.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
325.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
312.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

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
32.0ms
(* (tan x) (tan x))
25.0ms
(* (tan x) (tan x))
24.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
7.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
64.0ms
(* (tan x) (tan x))
48.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))
38.0ms
(* (tan x) (tan x))

simplify8.7s

Counts
131 → 157
Calls
131 calls:
Slowest
894.0ms
(* (+ (* 1 1) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))) (+ 1 (* (tan x) (tan x))))
581.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
532.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
485.0ms
(* (* (* (- 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))))))
442.0ms
(* (- (pow 1 3) (pow (* (tan x) (tan x)) 3)) 1)

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

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))

rewrite152.0ms

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))
14.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series244.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
64.0ms
(* (tan x) (tan x))
59.0ms
(* (tan x) (tan x))
58.0ms
(* (tan x) (tan x))

simplify5.3s

Counts
202 → 186
Calls
202 calls:
Slowest
440.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
388.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
324.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
324.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
269.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
39×*-un-lft-identity
32×add-cube-cbrt
30×times-frac
22×log-pow
21×exp-prod
19×pow1
14×difference-of-squares
10×add-cbrt-cube add-exp-log
8×tan-quot
6×swap-sqr associate-*r* associate-*l*
5×associate-/l*
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/r*
2×pow2 frac-times flip3-+ pow-plus div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv unswap-sqr associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-- exp-diff div-exp rem-log-exp flip--
Counts
4 → 142
Calls
4 calls:
Slowest
32.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
29.0ms
(* (tan x) (tan x))
28.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
107.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
49.0ms
(* (tan x) (tan x))
48.0ms
(* (tan x) (tan x))

simplify7.6s

Counts
132 → 154
Calls
132 calls:
Slowest
533.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
533.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
524.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
508.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
414.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes250.0ms

Accuracy

0% (0.4b remaining)

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

bsearch5.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.8s1561×body1280valid
1.4s4280×body80valid
1.2s1191×body640valid
603.0ms657×body320valid
133.0ms311×body160valid