Details

Time bar (total: 31.1s)

sample1.0s

Algorithm
intervals
Results
692.0ms48×body1280valid
67.0ms136×body80valid
47.0ms39×body640valid
20.0ms21×body320valid
8.0ms12×body160valid

simplify102.0ms

Calls
1 calls:
Slowest
102.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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

rewrite36.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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
12.0ms
(* (tan x) (tan x))
9.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms
(* (tan x) (tan x))
3.0ms
(- 1 (* (tan x) (tan x)))

series253.0ms

Calls
4 calls:
Slowest
105.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
77.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))
33.0ms
(- 1 (* (tan x) (tan x)))

simplify2.9s

Calls
72 calls:
Slowest
348.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
326.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
312.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
137.0ms
(/ (* (* (- 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)))))
116.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

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×expm1-log1p-u frac-times associate-*l/ prod-exp associate-/r/ insert-posit16 log1p-expm1-u 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
8.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))
1.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))

series253.0ms

Calls
4 calls:
Slowest
113.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
50.0ms
(* (tan x) (tan x))
50.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))
39.0ms
(* (tan x) (tan x))

simplify4.9s

Calls
68 calls:
Slowest
513.0ms
(* (+ (* 1 1) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))) (+ 1 (* (tan x) (tan x))))
498.0ms
(* (- (pow 1 3) (pow (* (tan x) (tan x)) 3)) (/ 1 (+ 1 (* (tan x) (tan x)))))
421.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
383.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
347.0ms
(* (* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x)))) (* (* (/ 1 (+ 1 (* (tan x) (tan x)))) (/ 1 (+ 1 (* (tan x) (tan x))))) (/ 1 (+ 1 (* (tan x) (tan x))))))

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.2b
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (fma (/ (sin x) (cos x)) (/ (sin x) (cos x)) 1))
0.2b
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
0.1b
(/ (sin x) (cos x))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
13×associate-*r* associate-*l*
9×pow1
6×cbrt-undiv associate-/r* div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg flip3-- flip-- associate-/l/
1×pow2 frac-times quot-tan sub-neg pow-plus div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative pow-prod-up
Calls
4 calls:
Slowest
20.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
10.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (fma (/ (sin x) (cos x)) (/ (sin x) (cos x)) 1))
4.0ms
(/ (sin x) (cos x))
2.0ms
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

series303.0ms

Calls
4 calls:
Slowest
150.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (fma (/ (sin x) (cos x)) (/ (sin x) (cos x)) 1))
66.0ms
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
57.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
30.0ms
(/ (sin x) (cos x))

simplify7.3s

Calls
106 calls:
Slowest
562.0ms
(/ (* (* (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))) (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))) (* (* (fma (/ (sin x) (cos x)) (/ (sin x) (cos x)) 1) (fma (/ (sin x) (cos x)) (/ (sin x) (cos x)) 1)) (fma (/ (sin x) (cos x)) (/ (sin x) (cos x)) 1)))
486.0ms
(- (* 1 1) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
401.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
367.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (fma (/ (sin x) (cos x)) (/ (sin x) (cos x)) 1))
348.0ms
(- (pow 1 3) (pow (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) 3))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

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))

rewrite53.0ms

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×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
Calls
4 calls:
Slowest
24.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
10.0ms
(* (tan x) (tan x))
8.0ms
(* (tan x) (tan x))
8.0ms
(* (tan x) (tan x))

series184.0ms

Calls
4 calls:
Slowest
56.0ms
(* (tan x) (tan x))
48.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
47.0ms
(* (tan x) (tan x))
33.0ms
(* (tan x) (tan x))

simplify1.9s

Calls
132 calls:
Slowest
149.0ms
(* (* (* (* (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))))
114.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
101.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
64.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes333.0ms

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
2.2s1447×body1280valid
1.9s1343×body640valid
946.0ms4279×body80valid
538.0ms301×body160valid
470.0ms630×body320valid