Details

Time bar (total: 40.2s)

sample454.0ms

Algorithm
intervals
Results
88.0ms51×body1280valid
52.0ms44×body640valid
30.0ms133×body80valid
18.0ms22×body320valid
3.0ms6×body160valid

simplify153.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
152.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

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)))

rewrite79.0ms

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
26.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
24.0ms
(* (tan x) (tan x))
16.0ms
(* (tan x) (tan x))
8.0ms
(- 1 (* (tan x) (tan x)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
270.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
81.0ms
(* (tan x) (tan x))
60.0ms
(* (tan x) (tan x))
50.0ms
(- 1 (* (tan x) (tan x)))

simplify6.9s

Counts
111 → 126
Calls
111 calls:
Slowest
945.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
607.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
606.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
416.0ms
(/ (* (* (- 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)))))
345.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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))))

rewrite86.0ms

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×associate-/r/ insert-posit16 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 → 134
Calls
4 calls:
Slowest
28.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
27.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))
13.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
98.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
52.0ms
(* (tan x) (tan x))
50.0ms
(* (tan x) (tan x))

simplify8.3s

Counts
132 → 146
Calls
132 calls:
Slowest
672.0ms
(/ (- 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))
589.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
589.0ms
(/ (* (* (- 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)))))
562.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

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))

rewrite153.0ms

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×*-commutative insert-posit16 add-log-exp unswap-sqr
Counts
4 → 166
Calls
4 calls:
Slowest
102.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
21.0ms
(* (tan x) (tan x))
13.0ms
(* (tan x) (tan x))
13.0ms
(* (tan x) (tan x))

series180.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
56.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
47.0ms
(* (tan x) (tan x))
40.0ms
(* (tan x) (tan x))
36.0ms
(* (tan x) (tan x))

simplify5.0s

Counts
202 → 178
Calls
202 calls:
Slowest
398.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
394.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
351.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
255.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
241.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

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))

rewrite183.0ms

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×*-commutative insert-posit16 add-log-exp unswap-sqr
Counts
4 → 166
Calls
4 calls:
Slowest
122.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
27.0ms
(* (tan x) (tan x))
18.0ms
(* (tan x) (tan x))
13.0ms
(* (tan x) (tan x))

series221.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
60.0ms
(* (tan x) (tan x))
55.0ms
(* (tan x) (tan x))
42.0ms
(* (tan x) (tan x))

simplify5.1s

Counts
202 → 178
Calls
202 calls:
Slowest
449.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
390.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
325.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
288.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
229.0ms
(+ (* 6/5 (pow x 8)) (+ (pow x 4) (* 4/3 (pow x 6))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.7s1561×body1280valid
1.2s1191×body640valid
920.0ms4280×body80valid
760.0ms311×body160valid
475.0ms657×body320valid