Details

Time bar (total: 1.7m)

sample298.0ms

Algorithm
intervals
Results
66.0ms48×body1280valid
41.0ms39×body640valid
31.0ms136×body80valid
15.0ms21×body320valid
5.0ms12×body160valid

simplify95.0ms

Calls
1 calls:
Slowest
94.0ms
(/ (- 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

localize25.0ms

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)))

rewrite96.0ms

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
Calls
4 calls:
Slowest
30.0ms
(* (tan x) (tan x))
28.0ms
(* (tan x) (tan x))
26.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms
(- 1 (* (tan x) (tan x)))

series265.0ms

Calls
4 calls:
Slowest
124.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
52.0ms
(* (tan x) (tan x))
46.0ms
(- 1 (* (tan x) (tan x)))
43.0ms
(* (tan x) (tan x))

simplify6.4s

Calls
111 calls:
Slowest
607.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
570.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
564.0ms
(/ (* (* (- 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)))))
494.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
336.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

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

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
95×times-frac
75×*-un-lft-identity
70×add-cube-cbrt
30×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
18×pow1
10×difference-of-squares
9×cbrt-undiv div-exp div-inv
8×prod-exp cbrt-unprod unswap-sqr
6×add-log-exp
5×associate-/l*
4×insert-posit16
3×associate-/r*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up flip-- associate-/l/
1×clear-num sub-neg frac-2neg flip3-+ diff-log div-sub flip-+
Calls
4 calls:
Slowest
36.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
28.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
22.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
6.0ms
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

series322.0ms

Calls
4 calls:
Slowest
133.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
73.0ms
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
60.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
56.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify15.4s

Calls
215 calls:
Slowest
691.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
638.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
599.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (cbrt (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))))
547.0ms
(- (pow 1 3) (pow (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) 3))
436.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
9×frac-times associate-*r*
8×flip3-+ flip-+ associate-/l/
7×associate-*l*
6×flip3-- flip-- add-log-exp
5×associate-*l/ associate-*r/
4×tan-quot insert-posit16
3×associate-/r* times-frac swap-sqr prod-exp cbrt-unprod
2×distribute-rgt-in cbrt-undiv sub-neg distribute-lft-in div-exp pow-prod-down associate-/r/ *-commutative distribute-lft-out difference-of-squares unswap-sqr
1×pow2 +-commutative clear-num sum-log frac-2neg pow-plus pow-sqr pow-prod-up div-inv associate-/l* distribute-lft-out--
Calls
4 calls:
Slowest
39.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
37.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
13.0ms
(* (tan x) (tan x))
8.0ms
(+ 1 (tan x))

series305.0ms

Calls
4 calls:
Slowest
152.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
78.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
39.0ms
(* (tan x) (tan x))
35.0ms
(+ 1 (tan x))

simplify11.9s

Calls
92 calls:
Slowest
697.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
554.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
550.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
506.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
500.0ms
(* (+ 1 (tan x)) (- (pow 1 3) (pow (tan x) 3)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

9.1b
(cbrt (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

rewrite420.0ms

Algorithm
rewrite-expression-head
Rules
158×add-cbrt-cube add-exp-log
148×frac-times
129×pow1
88×associate-*l/
84×add-sqr-sqrt
80×times-frac
76×associate-*r/
73×prod-exp cbrt-unprod
63×cbrt-div
60×*-un-lft-identity add-cube-cbrt
48×cbrt-undiv div-exp
38×pow-prod-up
27×swap-sqr associate-*r* associate-*l*
25×pow-prod-down
24×pow-sqr
20×pow-plus
15×pow2
9×unswap-sqr
8×div-inv
4×insert-posit16 add-log-exp
3×*-commutative
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
255.0ms
(cbrt (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
101.0ms
(* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
31.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
18.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series315.0ms

Calls
4 calls:
Slowest
107.0ms
(* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))
83.0ms
(cbrt (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
69.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
55.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify54.9s

Calls
388 calls:
Slowest
1.1s
(* (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)))))
953.0ms
(cbrt (* (* (* (sin x) (/ (sin x) (cos x))) (* (sin x) (sin x))) (* (/ (sin x) (cos x)) (sin x))))
850.0ms
(* (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)))) (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)))))
769.0ms
(cbrt (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (sin x) (sin x))) (* (sin x) (sin x))))
751.0ms
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)))) (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))

prune3.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes343.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch3.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.3s1447×body1280valid
1.6s1343×body640valid
897.0ms4279×body80valid
398.0ms630×body320valid
154.0ms301×body160valid