Details

Time bar (total: 1.0m)

sample307.0ms

Algorithm
intervals
Results
72.0ms44×body1280valid
51.0ms43×body640valid
36.0ms138×body80valid
15.0ms19×body320valid
7.0ms12×body160valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
140.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

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

rewrite66.0ms

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
23.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
21.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (* (tan x) (tan x)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
51.0ms
(* (tan x) (tan x))
50.0ms
(- 1 (* (tan x) (tan x)))
34.0ms
(* (tan x) (tan x))

simplify6.4s

Counts
111 → 126
Calls
111 calls:
Slowest
641.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
631.0ms
(/ (* (* (- 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))
509.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
321.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (* (tan x) (tan x)) 3)
0.4b
(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
236×tan-quot
130×pow1
97×frac-times
78×associate-*l/ associate-*r/
45×frac-sub
38×pow-prod-up
25×pow-prod-down
24×pow-sqr
21×add-cbrt-cube add-exp-log
20×pow-plus
15×pow2
14×sub-div
11×add-sqr-sqrt
10×prod-exp cbrt-unprod
9×*-un-lft-identity add-cube-cbrt
6×pow-pow add-log-exp
4×swap-sqr associate-*r* associate-*l* insert-posit16
3×cube-div pow-unpow
2×pow-exp *-commutative rem-cube-cbrt unswap-sqr
1×cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- diff-log unpow3 cube-prod flip-- difference-of-squares sqr-pow
Counts
4 → 211
Calls
4 calls:
Slowest
158.0ms
(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
92.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
27.0ms
(* (tan x) (tan x))
11.0ms
(pow (* (tan x) (tan x)) 3)

series288.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
89.0ms
(pow (* (tan x) (tan x)) 3)
58.0ms
(* (tan x) (tan x))
50.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify25.6s

Counts
290 → 223
Calls
290 calls:
Slowest
909.0ms
(- (* (* (* (tan x) (tan x)) (* (sin x) (tan x))) (* (cos x) (cos x))) (* (cos x) (* (sin x) (sin x))))
630.0ms
(- (/ (pow (sin x) 4) (pow (cos x) 4)) (/ (pow (sin x) 2) (pow (cos x) 2)))
599.0ms
(- (/ (pow (sin x) 4) (pow (cos x) 4)) (/ (pow (sin x) 2) (pow (cos x) 2)))
498.0ms
(- (* (* (* (tan x) (tan x)) (* (tan x) (sin x))) (* (cos x) (cos x))) (* (cos x) (* (sin x) (sin x))))
441.0ms
(- (* (* (* (sin x) (tan x)) (* (tan x) (tan x))) (* (cos x) (cos x))) (* (cos x) (* (sin x) (sin x))))

prune2.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.2b
(- 1 (* (tan x) (tan x)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×*-un-lft-identity
22×log-pow add-cube-cbrt
21×exp-prod
19×pow1
15×times-frac
8×add-cbrt-cube tan-quot add-exp-log difference-of-squares
6×swap-sqr associate-*r* associate-*l* add-log-exp
4×insert-posit16
3×log-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×log-div sub-neg flip3-+ flip3-- exp-diff diff-log div-sub rem-log-exp flip-+ div-inv flip--
Counts
4 → 108
Calls
4 calls:
Slowest
33.0ms
(* (tan x) (tan x))
33.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
28.0ms
(* (tan x) (tan x))
9.0ms
(- 1 (* (tan x) (tan x)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
49.0ms
(* (tan x) (tan x))
46.0ms
(* (tan x) (tan x))
42.0ms
(- 1 (* (tan x) (tan x)))

simplify5.1s

Counts
93 → 120
Calls
93 calls:
Slowest
626.0ms
(/ (- 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))
464.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
320.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
271.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
61×*-un-lft-identity
54×add-sqr-sqrt
43×times-frac
38×add-cube-cbrt
34×log-pow
32×exp-prod
27×associate-*l*
23×associate-*r*
15×pow1
11×add-cbrt-cube add-exp-log
9×log-prod
7×distribute-lft-out
6×add-log-exp difference-of-squares
4×tan-quot insert-posit16
3×distribute-rgt-in distribute-lft-in swap-sqr prod-exp cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
2×flip3-+ pow-prod-down associate-*l/ associate-/r/ *-commutative flip-+
1×pow2 frac-times cbrt-undiv +-commutative sum-log pow-plus div-exp rem-log-exp associate-*r/ pow-sqr pow-prod-up
Counts
4 → 138
Calls
4 calls:
Slowest
101.0ms
(* (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))) (log (exp (/ (+ 1 (tan x)) 1))))
31.0ms
(* (tan x) (tan x))
15.0ms
(log (exp (/ (+ 1 (tan x)) 1)))
4.0ms
(+ 1 (tan x))

series241.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(* (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))) (log (exp (/ (+ 1 (tan x)) 1))))
50.0ms
(* (tan x) (tan x))
32.0ms
(+ 1 (tan x))
24.0ms
(log (exp (/ (+ 1 (tan x)) 1)))

simplify8.4s

Counts
118 → 150
Calls
118 calls:
Slowest
630.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
545.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
484.0ms
(/ (- 1 (tan x)) (+ (pow 1 3) (pow (* (tan x) (tan x)) 3)))
458.0ms
(* (- 1 (tan x)) (log (exp (/ (+ 1 (tan x)) 1))))
450.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes420.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
3.2s1561×body1280valid
1.3s1228×body640valid
951.0ms4261×body80valid
463.0ms612×body320valid
170.0ms338×body160valid