Details

Time bar (total: 28.6s)

sample312.0ms

Algorithm
intervals
Results
76.0ms47×body1280valid
68.0ms16×body320valid
50.0ms44×body640valid
33.0ms143×body80valid
3.0ms6×body160valid

simplify555.0ms

Calls
1 calls:
Slowest
554.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

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)))

rewrite44.0ms

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
11.0ms
(* (tan x) (tan x))
8.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
8.0ms
(* (tan x) (tan x))
3.0ms
(- 1 (* (tan x) (tan x)))

series213.0ms

Calls
4 calls:
Slowest
98.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
54.0ms
(* (tan x) (tan x))
39.0ms
(* (tan x) (tan x))
22.0ms
(- 1 (* (tan x) (tan x)))

simplify3.3s

Calls
72 calls:
Slowest
511.0ms
(/ (* (* (- 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)))))
444.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
388.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
324.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
118.0ms
(- 1 (+ (pow x 2) (* 2/3 (pow x 4))))

prune929.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
76×pow1
44×tan-quot
26×pow-prod-up
22×add-cbrt-cube add-exp-log
21×pow-prod-down
20×frac-times
15×pow-plus
14×associate-*l/ associate-*r/
12×pow2
11×prod-exp cbrt-unprod
10×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×*-commutative insert-posit16 add-log-exp
Calls
4 calls:
Slowest
26.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
10.0ms
(* (tan x) (tan x))
9.0ms
(* (tan x) (tan x))
9.0ms
(* (tan x) (tan x))

series177.0ms

Calls
4 calls:
Slowest
60.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
43.0ms
(* (tan x) (tan x))
42.0ms
(* (tan x) (tan x))
32.0ms
(* (tan x) (tan x))

simplify2.0s

Calls
132 calls:
Slowest
145.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
145.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
142.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
141.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
59.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
13×add-exp-log
12×associate-*r*
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×add-cbrt-cube
9×associate-*l*
8×tan-quot
4×frac-times associate-*l/ prod-exp associate-/r/ insert-posit16 add-log-exp
3×associate-/r* pow-prod-down associate-*r/ *-commutative cbrt-unprod
2×pow2 rec-exp flip3-+ pow-plus flip3-- pow-prod-up flip-+ div-inv flip--
1×clear-num frac-2neg un-div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
11.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
9.0ms
(* (tan x) (tan x))
7.0ms
(* (tan x) (tan x))
2.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))

series241.0ms

Calls
4 calls:
Slowest
96.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
55.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))
47.0ms
(* (tan x) (tan x))
43.0ms
(* (tan x) (tan x))

simplify4.8s

Calls
68 calls:
Slowest
496.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
487.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
460.0ms
(* (+ (* 1 1) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))) (+ 1 (* (tan x) (tan x))))
452.0ms
(* (- (pow 1 3) (pow (* (tan x) (tan x)) 3)) (/ 1 (+ 1 (* (tan x) (tan x)))))
397.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))

prune916.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.2b
(* (sin x) (tan x))
0.2b
(* (- 1 (/ (* (sin x) (tan x)) (cos x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
0.2b
(/ (* (sin x) (tan x)) (cos x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
15×add-cbrt-cube
13×pow1
12×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
9×associate-*l*
6×tan-quot
5×prod-exp
4×associate-*r/ cbrt-unprod insert-posit16 add-log-exp
3×frac-times associate-/r* times-frac pow-prod-down associate-*l/ *-commutative
2×cbrt-undiv flip3-- div-exp associate-/r/ div-inv flip--
1×pow2 rec-exp clear-num frac-2neg flip3-+ pow-plus un-div-inv pow-prod-up flip-+ associate-/l* associate-/l/
Calls
4 calls:
Slowest
9.0ms
(* (tan x) (tan x))
8.0ms
(/ (* (sin x) (tan x)) (cos x))
7.0ms
(* (sin x) (tan x))
7.0ms
(* (- 1 (/ (* (sin x) (tan x)) (cos x))) (/ 1 (+ 1 (* (tan x) (tan x)))))

series251.0ms

Calls
4 calls:
Slowest
97.0ms
(* (- 1 (/ (* (sin x) (tan x)) (cos x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
69.0ms
(/ (* (sin x) (tan x)) (cos x))
59.0ms
(* (sin x) (tan x))
26.0ms
(* (tan x) (tan x))

simplify5.5s

Calls
71 calls:
Slowest
601.0ms
(* (- (pow 1 3) (pow (/ (* (sin x) (tan x)) (cos x)) 3)) (/ 1 (+ 1 (* (tan x) (tan x)))))
518.0ms
(* (- (pow 1 3) (pow (/ (* (sin x) (tan x)) (cos x)) 3)) 1)
486.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
465.0ms
(* (* (* (- 1 (/ (* (sin x) (tan x)) (cos x))) (- 1 (/ (* (sin x) (tan x)) (cos x)))) (- 1 (/ (* (sin x) (tan x)) (cos x)))) (* (* (/ 1 (+ 1 (* (tan x) (tan x)))) (/ 1 (+ 1 (* (tan x) (tan x))))) (/ 1 (+ 1 (* (tan x) (tan x))))))
428.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes174.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.8s1506×body1280valid
1.5s4295×body80valid
1.3s1246×body640valid
444.0ms646×body320valid
135.0ms307×body160valid