Details

Time bar (total: 26.7s)

sample429.0ms

Algorithm
intervals
Results
115.0ms46×body1280valid
41.0ms31×body640valid
40.0ms154×body80valid
16.0ms19×body320valid
3.0ms6×body160valid

simplify133.0ms

Calls
1 calls:
Slowest
133.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.1b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×pow1
10×add-cbrt-cube add-exp-log
9×times-frac
8×tan-quot
6×associate-*r* associate-*l*
4×insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative pow-prod-up cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ div-sub div-exp flip-+ div-inv
Calls
4 calls:
Slowest
28.0ms
(* (tan x) (tan x))
10.0ms
(* (tan x) (tan x))
9.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
3.0ms
(- 1 (* (tan x) (tan x)))

series215.0ms

Calls
4 calls:
Slowest
95.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
47.0ms
(* (tan x) (tan x))
43.0ms
(* (tan x) (tan x))
29.0ms
(- 1 (* (tan x) (tan x)))

simplify3.7s

Calls
72 calls:
Slowest
542.0ms
(/ (* (* (- 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)))))
506.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
390.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
361.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
125.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune949.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.2b
(/ (sin x) (cos x))
0.2b
(/ (sin x) (cos x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
48×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
26×associate-*r* associate-*l*
14×pow1
10×cbrt-undiv div-exp
8×prod-exp cbrt-unprod
6×associate-/r* div-inv associate-/l*
4×insert-posit16 add-log-exp
2×pow2 frac-times quot-tan clear-num frac-2neg pow-plus pow-prod-down associate-*l/ associate-*r/ *-commutative pow-prod-up
Calls
4 calls:
Slowest
10.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
9.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
7.0ms
(/ (sin x) (cos x))
7.0ms
(/ (sin x) (cos x))

series148.0ms

Calls
4 calls:
Slowest
49.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
34.0ms
(/ (sin x) (cos x))
33.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
32.0ms
(/ (sin x) (cos x))

simplify4.0s

Calls
144 calls:
Slowest
261.0ms
(* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))))
233.0ms
(* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))))
200.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))))
197.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))))
178.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
14×add-sqr-sqrt *-un-lft-identity
12×tan-quot
10×add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
6×add-log-exp
4×distribute-rgt-out-- associate-/r/ insert-posit16 div-inv
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod
2×flip3-+ flip-+ distribute-lft-out-- difference-of-squares
1×sub-neg times-frac flip3-- diff-log frac-sub flip-- sub-div
Calls
4 calls:
Slowest
14.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
10.0ms
(* (tan x) (tan x))
9.0ms
(* (tan x) (tan x))
9.0ms
(* (tan x) (tan x))

series214.0ms

Calls
4 calls:
Slowest
121.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
37.0ms
(* (tan x) (tan x))
32.0ms
(* (tan x) (tan x))
25.0ms
(* (tan x) (tan x))

simplify2.9s

Calls
76 calls:
Slowest
513.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
302.0ms
(- (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)) (/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))))
265.0ms
(- (* 1 (+ 1 (* (tan x) (tan x)))) (* (+ 1 (* (tan x) (tan x))) (* (tan x) (tan x))))
251.0ms
(- (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)) (/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))))
172.0ms
(- (/ 1 (- (* 1 1) (* (* (tan x) (tan x)) (* (tan x) (tan x))))) (/ (* (tan x) (tan x)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan x) (tan x))))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
128×pow1
72×tan-quot
48×pow-prod-up
38×pow-prod-down
36×frac-times
32×add-cbrt-cube add-exp-log
26×pow-plus
24×associate-*l/ associate-*r/
20×pow2
18×prod-exp cbrt-unprod
8×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×*-commutative insert-posit16 add-log-exp
Calls
4 calls:
Slowest
38.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
22.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
6.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))

series162.0ms

Calls
4 calls:
Slowest
58.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
44.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
35.0ms
(* (tan x) (tan x))
25.0ms
(* (tan x) (tan x))

simplify3.2s

Calls
192 calls:
Slowest
170.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
153.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
138.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
129.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
129.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes278.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.0s1524×body1280valid
1.7s1201×body640valid
997.0ms4337×body80valid
499.0ms662×body320valid
105.0ms276×body160valid