Details

Time bar (total: 58.9s)

sample371.0ms

Algorithm
intervals
Results
142.0ms7×body160valid
68.0ms48×body1280valid
42.0ms22×body320valid
35.0ms43×body640valid
23.0ms136×body80valid

simplify119.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
119.0ms
(/ (- 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

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

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
32.0ms
(* (tan x) (tan x))
29.0ms
(* (tan x) (tan x))
20.0ms
(- 1 (* (tan x) (tan x)))
15.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
68.0ms
(* (tan x) (tan x))
57.0ms
(* (tan x) (tan x))
40.0ms
(- 1 (* (tan x) (tan x)))

simplify5.8s

Counts
119 → 140
Calls
119 calls:
Slowest
551.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
489.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
359.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
322.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
311.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
39×*-un-lft-identity
31×add-cube-cbrt
27×prod-diff
13×pow1 add-cbrt-cube add-exp-log
11×distribute-rgt-in distribute-lft-in
9×frac-times associate-*r*
8×associate-/l/
7×flip3-+ flip3-- associate-*l* flip-+ flip--
6×add-log-exp
5×associate-*l/ associate-*r/
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* sub-neg times-frac fma-neg swap-sqr prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down associate-/r/ *-commutative distribute-lft-out-- unswap-sqr
1×pow2 clear-num frac-2neg pow-plus diff-log pow-sqr pow-prod-up div-inv distribute-lft-out associate-/l*
Counts
4 → 150
Calls
4 calls:
Slowest
44.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
30.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
17.0ms
(* (tan x) (tan x))
16.0ms
(- 1 (tan x))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
76.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
39.0ms
(* (tan x) (tan x))
31.0ms
(- 1 (tan x))

simplify21.7s

Counts
134 → 162
Calls
134 calls:
Slowest
1.0s
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
983.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
947.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
916.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
723.0ms
(* (fma (- (tan x)) 1 (* (tan x) 1)) (+ 1 (tan x)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
26×add-cube-cbrt
21×prod-diff
13×pow1 add-cbrt-cube add-exp-log
12×times-frac
6×associate-*r* associate-*l* tan-quot add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×associate-/r* fma-neg swap-sqr associate-*l/ prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative difference-of-squares unswap-sqr
1×pow2 frac-times clear-num sub-neg frac-2neg pow-plus flip3-- diff-log associate-*r/ pow-sqr pow-prod-up flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 120
Calls
4 calls:
Slowest
24.0ms
(* (tan x) (tan x))
19.0ms
(/ (* (tan x) (sin x)) (cos x))
14.0ms
(* (tan x) (sin x))
10.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(/ (* (tan x) (sin x)) (cos x))
65.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))
62.0ms
(* (tan x) (sin x))
48.0ms
(* (tan x) (tan x))

simplify11.5s

Counts
113 → 132
Calls
113 calls:
Slowest
638.0ms
(fma (- (/ 1 (cos x))) (* (tan x) (sin x)) (* (/ 1 (cos x)) (* (tan x) (sin x))))
311.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
311.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
303.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))
303.0ms
(fma 1 1 (- (* (/ 1 (cos x)) (* (tan x) (sin x)))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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))

rewrite151.0ms

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
81.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
29.0ms
(* (tan x) (tan x))
21.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))

series203.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(* (tan x) (tan x))
59.0ms
(* (tan x) (tan x))
50.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
32.0ms
(* (tan x) (tan x))

simplify5.2s

Counts
202 → 186
Calls
202 calls:
Slowest
407.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
395.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
313.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
257.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
249.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes273.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.9s1488×body1280valid
1.6s1201×body640valid
885.0ms4378×body80valid
444.0ms625×body320valid
169.0ms308×body160valid