Details

Time bar (total: 1.1m)

sample519.0ms

Algorithm
intervals
Results
202.0ms45×body1280valid
142.0ms42×body640valid
39.0ms142×body80valid
15.0ms19×body320valid
4.0ms8×body160valid

simplify77.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
76.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

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)))

rewrite109.0ms

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
29.0ms
(* (tan x) (tan x))
28.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
26.0ms
(* (tan x) (tan x))
19.0ms
(- 1 (* (tan x) (tan x)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
74.0ms
(* (tan x) (tan x))
64.0ms
(- 1 (* (tan x) (tan x)))
57.0ms
(* (tan x) (tan x))

simplify6.5s

Counts
111 → 126
Calls
111 calls:
Slowest
626.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
614.0ms
(/ (* (* (- 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)))))
603.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
487.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
309.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
183×*-un-lft-identity
133×add-sqr-sqrt
83×add-cube-cbrt
32×difference-of-squares
26×distribute-lft-out
24×associate-/r*
16×distribute-lft-out--
11×pow1 add-cbrt-cube add-exp-log associate-/r/
8×add-log-exp
6×flip3-- div-inv flip--
4×tan-quot insert-posit16 associate-/l*
3×cbrt-undiv swap-sqr div-exp associate-*r* associate-*l*
2×flip3-+ flip-+ associate-/l/
1×pow2 frac-times +-commutative clear-num sum-log sub-neg frac-2neg pow-plus diff-log pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
4 → 200
Calls
4 calls:
Slowest
51.0ms
(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
13.0ms
(* (tan x) (tan x))
8.0ms
(+ 1 (tan x))
4.0ms
(- 1 (tan x))

series267.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
55.0ms
(* (tan x) (tan x))
36.0ms
(- 1 (tan x))
18.0ms
(+ 1 (tan x))

simplify26.0s

Counts
270 → 212
Calls
270 calls:
Slowest
712.0ms
(/ (* (cbrt (+ 1 (tan x))) (cbrt (+ 1 (tan x)))) (/ (+ 1 (* (tan x) (tan x))) (- (* 1 1) (* (tan x) (tan x)))))
562.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
480.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
480.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
469.0ms
(/ (sqrt (+ 1 (tan x))) (/ (+ 1 (* (tan x) (tan x))) (- (pow 1 3) (pow (tan x) 3))))

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

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

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×*-un-lft-identity
21×add-cube-cbrt
18×times-frac
13×pow1
10×add-cbrt-cube add-exp-log difference-of-squares
6×associate-*r* associate-*l* associate-/l* add-log-exp
5×tan-quot distribute-lft-out--
4×insert-posit16
3×associate-/r* swap-sqr
2×flip3-- pow-prod-down prod-exp associate-*r/ associate-/r/ *-commutative cbrt-unprod flip-- unswap-sqr associate-/l/
1×pow2 frac-times cbrt-undiv clear-num sub-neg frac-2neg flip3-+ pow-plus diff-log div-sub div-exp associate-*l/ pow-sqr pow-prod-up flip-+ div-inv
Counts
4 → 110
Calls
4 calls:
Slowest
36.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
27.0ms
(* (tan x) (tan x))
25.0ms
(* (sin x) (tan x))
16.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
79.0ms
(* (sin x) (tan x))
70.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))
65.0ms
(* (tan x) (tan x))

simplify9.2s

Counts
104 → 122
Calls
104 calls:
Slowest
667.0ms
(- (pow 1 3) (pow (/ (* (sin x) (tan x)) (cos x)) 3))
608.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
588.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
468.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
304.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
42×add-sqr-sqrt
24×times-frac
20×add-cube-cbrt
12×difference-of-squares
10×add-cbrt-cube add-exp-log
8×pow1
7×distribute-lft-out
6×associate-*r* associate-*l* associate-/l* distribute-lft-out-- add-log-exp
4×associate-/r* insert-posit16
2×flip3-- pow-prod-down prod-exp tan-quot associate-*r/ associate-/r/ *-commutative 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 → 108
Calls
4 calls:
Slowest
35.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (/ (* (sin x) (tan x)) (cos x))))
12.0ms
(* (sin x) (tan x))
11.0ms
(* (sin x) (tan x))
8.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (/ (* (sin x) (tan x)) (cos x))))
66.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))
62.0ms
(* (sin x) (tan x))
54.0ms
(* (sin x) (tan x))

simplify11.4s

Counts
103 → 120
Calls
103 calls:
Slowest
694.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
658.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
646.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (/ (* (sin x) (tan x)) (cos x))))
604.0ms
(- (pow 1 3) (pow (/ (* (sin x) (tan x)) (cos x)) 3))
412.0ms
(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (/ (* (sin x) (tan x)) (cos x))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.2s1433×body1280valid
2.0s1218×body640valid
880.0ms4397×body80valid
528.0ms625×body320valid
181.0ms327×body160valid