Details

Time bar (total: 1.4m)

sample417.0ms

Algorithm
intervals
Results
105.0ms45×body1280valid
48.0ms42×body640valid
39.0ms142×body80valid
15.0ms19×body320valid
4.0ms8×body160valid

simplify1.0s

Counts
1 → 1
Calls
1 calls:
Slowest
99.0ms
(/ (- 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

localize45.0ms

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)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
24×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×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg prod-diff
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 → 128
Calls
4 calls:
Slowest
32.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(- 1 (* (tan x) (tan x)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
60.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))
36.0ms
(- 1 (* (tan x) (tan x)))

simplify5.8s

Counts
119 → 140
Calls
119 calls:
Slowest
577.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
565.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
321.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
308.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
292.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
191×*-un-lft-identity
186×times-frac
141×add-sqr-sqrt
91×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/
9×prod-diff
8×add-log-exp
6×flip3-- div-inv flip--
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u associate-/l*
3×cbrt-undiv fma-def fma-neg 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 → 223
Calls
4 calls:
Slowest
38.0ms
(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
14.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (tan x))
4.0ms
(+ 1 (tan x))

series254.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(/ (+ 1 (tan x)) (/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x))))
40.0ms
(* (tan x) (tan x))
36.0ms
(- 1 (tan x))
25.0ms
(+ 1 (tan x))

simplify27.7s

Counts
292 → 235
Calls
292 calls:
Slowest
506.0ms
(/ (sqrt (+ 1 (tan x))) (/ (+ 1 (* (tan x) (tan x))) (- (pow 1 3) (pow (tan x) 3))))
499.0ms
(/ (* (cbrt (+ 1 (tan x))) (cbrt (+ 1 (tan x)))) (/ (* (cbrt (+ 1 (* (tan x) (tan x)))) (cbrt (+ 1 (* (tan x) (tan x))))) (+ (sqrt 1) (sqrt (tan x)))))
457.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
411.0ms
(/ (* (cbrt (+ 1 (tan x))) (cbrt (+ 1 (tan x)))) (/ (* (cbrt (+ 1 (* (tan x) (tan x)))) (cbrt (+ 1 (* (tan x) (tan x))))) (+ 1 (sqrt (tan x)))))
381.0ms
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- (pow 1 3) (pow (tan x) 3))))

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
50×*-un-lft-identity
35×add-cube-cbrt
27×times-frac
21×prod-diff
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×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×associate-/r* fma-neg swap-sqr
2×flip3-- pow-prod-down associate-*l/ prod-exp 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-*r/ pow-sqr pow-prod-up flip-+
Counts
4 → 142
Calls
4 calls:
Slowest
38.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
20.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (sin x))
10.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
70.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))
58.0ms
(* (tan x) (sin x))
47.0ms
(* (tan x) (tan x))

simplify17.4s

Counts
148 → 154
Calls
148 calls:
Slowest
583.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
523.0ms
(- (pow 1 3) (pow (/ (* (tan x) (sin x)) (cos x)) 3))
490.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
489.0ms
(/ (- (sqrt 1) (sqrt (/ (* (tan x) (sin x)) (cos x)))) (+ 1 (* (tan x) (tan x))))
330.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
56×add-sqr-sqrt
34×add-cube-cbrt
33×times-frac
21×prod-diff
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×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u div-inv
3×fma-neg
2×flip3-- pow-prod-down associate-*l/ prod-exp tan-quot 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-+
Counts
4 → 140
Calls
4 calls:
Slowest
71.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (/ (* (tan x) (sin x)) (cos x))))
31.0ms
(* (tan x) (sin x))
26.0ms
(* (tan x) (sin x))
20.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (/ (* (tan x) (sin x)) (cos x))))
84.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))
84.0ms
(* (tan x) (sin x))
63.0ms
(* (tan x) (sin x))

simplify18.8s

Counts
147 → 152
Calls
147 calls:
Slowest
566.0ms
(- (pow 1 3) (pow (/ (* (tan x) (sin x)) (cos x)) 3))
477.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
442.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
361.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (sin x) (sin x)) (sin x)))
342.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (/ (* (tan x) (sin x)) (cos x))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

0% (0.3b remaining)

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

bsearch8.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.6s1433×body1280valid
1.1s1218×body640valid
837.0ms4397×body80valid
412.0ms625×body320valid
117.0ms327×body160valid