Details

Time bar (total: 51.7s)

sample449.0ms

Algorithm
intervals
Results
68.0ms42×body640valid
56.0ms48×body1280valid
26.0ms142×body80valid
13.0ms18×body320valid
2.0ms6×body160valid

simplify69.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
69.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.1b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite68.0ms

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))))
17.0ms
(* (tan x) (tan x))
16.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (* (tan x) (tan x)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
53.0ms
(* (tan x) (tan x))
53.0ms
(- 1 (* (tan x) (tan x)))
38.0ms
(* (tan x) (tan x))

simplify6.4s

Counts
111 → 126
Calls
111 calls:
Slowest
617.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
597.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
556.0ms
(/ (* (* (- 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)))))
532.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
307.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.2b
(/ (* (sin x) (tan x)) (cos x))
0.2b
(* (sin x) (tan x))
0.1b
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×*-un-lft-identity
23×add-cube-cbrt
21×times-frac
15×add-cbrt-cube add-exp-log
13×pow1
8×difference-of-squares
7×associate-/l*
6×associate-/r* associate-*r* associate-*l* tan-quot
4×insert-posit16 distribute-lft-out-- add-log-exp
3×cbrt-undiv swap-sqr div-exp prod-exp associate-*r/ cbrt-unprod associate-/l/
2×clear-num frac-2neg pow-prod-down associate-/r/ *-commutative div-inv unswap-sqr
1×pow2 frac-times flip3-+ pow-plus flip3-- div-sub associate-*l/ pow-sqr pow-prod-up flip-+ flip--
Counts
4 → 117
Calls
4 calls:
Slowest
42.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
27.0ms
(* (tan x) (tan x))
16.0ms
(/ (* (sin x) (tan x)) (cos x))
11.0ms
(* (sin x) (tan x))

series364.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
89.0ms
(/ (* (sin x) (tan x)) (cos x))
61.0ms
(* (sin x) (tan x))
57.0ms
(* (tan x) (tan x))

simplify9.6s

Counts
113 → 129
Calls
113 calls:
Slowest
671.0ms
(/ (- 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))
595.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (sqrt (+ 1 (* (tan x) (tan x)))))
571.0ms
(- (pow 1 3) (pow (/ (* (sin x) (tan x)) (cos x)) 3))
542.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.2b
(* (* (sin x) (tan x)) (/ 1 (cos x)))
0.2b
(* (sin x) (tan x))
0.1b
(/ (- 1 (* (* (sin x) (tan x)) (/ 1 (cos x)))) (+ 1 (* (tan x) (tan x))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
29×add-sqr-sqrt
25×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube
19×associate-*r*
18×pow1 times-frac
14×prod-exp
8×cbrt-unprod
7×associate-*l* tan-quot
5×div-exp pow-prod-down associate-*r/
4×insert-posit16 add-log-exp
3×cbrt-undiv associate-/r* swap-sqr *-commutative associate-/l*
2×frac-times rec-exp 1-exp associate-*l/ associate-/r/ div-inv unswap-sqr associate-/l/
1×pow2 clear-num frac-2neg flip3-+ pow-plus flip3-- div-sub pow-sqr un-div-inv pow-prod-up flip-+ flip--
Counts
4 → 123
Calls
4 calls:
Slowest
32.0ms
(* (* (sin x) (tan x)) (/ 1 (cos x)))
21.0ms
(* (sin x) (tan x))
21.0ms
(* (tan x) (tan x))
20.0ms
(/ (- 1 (* (* (sin x) (tan x)) (/ 1 (cos x)))) (+ 1 (* (tan x) (tan x))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(/ (- 1 (* (* (sin x) (tan x)) (/ 1 (cos x)))) (+ 1 (* (tan x) (tan x))))
86.0ms
(* (* (sin x) (tan x)) (/ 1 (cos x)))
55.0ms
(* (sin x) (tan x))
43.0ms
(* (tan x) (tan x))

simplify12.9s

Counts
111 → 135
Calls
111 calls:
Slowest
762.0ms
(* (* (* (* (sin x) (sin x)) (sin x)) (* (* (tan x) (tan x)) (tan x))) (* (* (/ 1 (cos x)) (/ 1 (cos x))) (/ 1 (cos x))))
686.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
685.0ms
(- (* 1 1) (* (* (* (sin x) (tan x)) (/ 1 (cos x))) (* (* (sin x) (tan x)) (/ 1 (cos x)))))
602.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
544.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.2b
(* (* (sin x) (tan x)) (/ 1 (cos x)))
0.2b
(* (sin x) (tan x))
0.1b
(/ (sin x) (cos x))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
58×times-frac
49×*-un-lft-identity add-cube-cbrt
42×add-exp-log
32×add-cbrt-cube
29×associate-*r*
18×pow1
17×associate-*l* prod-exp
13×swap-sqr
11×cbrt-unprod
9×div-exp
7×cbrt-undiv
6×div-inv
5×pow-prod-down associate-*r/ unswap-sqr
4×insert-posit16 add-log-exp
3×associate-/r* tan-quot *-commutative associate-/l*
2×frac-times rec-exp 1-exp associate-*l/
1×pow2 quot-tan clear-num frac-2neg pow-plus pow-sqr un-div-inv pow-prod-up
Counts
4 → 158
Calls
4 calls:
Slowest
64.0ms
(* (* (sin x) (tan x)) (/ 1 (cos x)))
36.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
22.0ms
(* (sin x) (tan x))
16.0ms
(/ (sin x) (cos x))

series268.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(* (sin x) (tan x))
77.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
76.0ms
(* (* (sin x) (tan x)) (/ 1 (cos x)))
35.0ms
(/ (sin x) (cos x))

simplify8.3s

Counts
158 → 170
Calls
158 calls:
Slowest
840.0ms
(* (* (* (* (sin x) (sin x)) (sin x)) (* (* (tan x) (tan x)) (tan x))) (* (* (/ 1 (cos x)) (/ 1 (cos x))) (/ 1 (cos x))))
502.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))
362.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
339.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (tan x) (tan x)) (tan x)))
242.0ms
(* (* (* (* (sin x) (tan x)) (* (sin x) (tan x))) (* (sin x) (tan x))) (/ (* (* 1 1) 1) (* (* (cos x) (cos x)) (cos x))))

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes450.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
3.0s1509×body1280valid
1.3s1284×body640valid
937.0ms4271×body80valid
438.0ms625×body320valid
177.0ms311×body160valid