Details

Time bar (total: 1.2m)

sample309.0ms

Algorithm
intervals
Results
75.0ms46×body1280valid
46.0ms39×body640valid
35.0ms139×body80valid
19.0ms22×body320valid
6.0ms10×body160valid

simplify152.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
151.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

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

rewrite106.0ms

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
33.0ms
(* (tan x) (tan x))
29.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
29.0ms
(* (tan x) (tan x))
10.0ms
(- 1 (* (tan x) (tan x)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
81.0ms
(* (tan x) (tan x))
41.0ms
(- 1 (* (tan x) (tan x)))
40.0ms
(* (tan x) (tan x))

simplify5.8s

Counts
119 → 140
Calls
119 calls:
Slowest
535.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
532.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
366.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
352.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
325.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
27×prod-diff
13×pow1
11×distribute-rgt-in distribute-lft-in
9×associate-*r*
8×add-cbrt-cube add-exp-log add-log-exp
7×associate-*l*
5×frac-times
4×expm1-log1p-u flip3-+ flip3-- tan-quot flip-+ insert-posit16 log1p-expm1-u flip-- difference-of-squares
3×sub-neg fma-def fma-neg swap-sqr associate-*l/ associate-*r/
2×pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out-- unswap-sqr
1×pow2 +-commutative sum-log pow-plus diff-log pow-sqr pow-prod-up
Counts
4 → 134
Calls
4 calls:
Slowest
29.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
18.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (tan x))
5.0ms
(+ 1 (tan x))

series180.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
44.0ms
(* (tan x) (tan x))
23.0ms
(+ 1 (tan x))
22.0ms
(- 1 (tan x))

simplify16.6s

Counts
114 → 146
Calls
114 calls:
Slowest
1.0s
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
893.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
865.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
786.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
729.0ms
(* (fma (- (tan x)) 1 (* (tan x) 1)) (+ 1 (tan x)))

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
44×tan-quot
35×add-sqr-sqrt
30×*-un-lft-identity
29×frac-times
26×flip3-- flip--
23×pow1
22×frac-sub
21×add-cube-cbrt
20×associate-*r/
19×associate-*l/
15×prod-diff
13×add-cbrt-cube add-exp-log
12×associate-*l*
11×associate--l+
9×add-log-exp
7×associate-*r*
6×fma-neg swap-sqr difference-of-squares
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×diff-log *-commutative distribute-lft-out-- unswap-sqr
2×pow2 sub-neg pow-plus pow-sqr pow-prod-up sub-div
1×associate--l-
Counts
4 → 162
Calls
4 calls:
Slowest
98.0ms
(- (- 1 (tan x)) (* (- 1 (tan x)) (* (tan x) (tan x))))
96.0ms
(* (- 1 (tan x)) (* (tan x) (tan x)))
30.0ms
(* (tan x) (tan x))
28.0ms
(* (tan x) (tan x))

series268.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(- (- 1 (tan x)) (* (- 1 (tan x)) (* (tan x) (tan x))))
68.0ms
(* (- 1 (tan x)) (* (tan x) (tan x)))
55.0ms
(* (tan x) (tan x))
33.0ms
(* (tan x) (tan x))

simplify31.0s

Counts
167 → 174
Calls
167 calls:
Slowest
885.0ms
(* (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))) (* (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))) (cos x)))
866.0ms
(* (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))) (* (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))) (* (cos x) (cos x))))
851.0ms
(* (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))) (* (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))) (cos x)))
701.0ms
(fma (- (* (tan x) (tan x))) (- 1 (tan x)) (* (* (tan x) (tan x)) (- 1 (tan x))))
691.0ms
(fma (- (* (tan x) (tan x))) (- 1 (tan x)) (* (* (tan x) (tan x)) (- 1 (tan x))))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (* (tan x) (tan x)) 3)
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1
23×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
16×tan-quot
13×add-cbrt-cube add-exp-log
9×swap-sqr associate-*r* associate-*l*
6×pow-pow
4×pow2 expm1-log1p-u frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr pow-prod-up cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cube-div pow-unpow *-commutative unswap-sqr
2×pow-exp rem-cube-cbrt
1×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod sqr-pow
Counts
4 → 125
Calls
4 calls:
Slowest
16.0ms
(pow (* (tan x) (tan x)) 3)
16.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series185.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(pow (* (tan x) (tan x)) 3)
50.0ms
(* (tan x) (tan x))
38.0ms
(* (tan x) (tan x))
32.0ms
(* (tan x) (tan x))

simplify3.2s

Counts
104 → 137
Calls
104 calls:
Slowest
374.0ms
(+ (* 2 (pow x 8)) (+ (* 37/15 (pow x 10)) (pow x 6)))
267.0ms
(/ (pow (sin x) 6) (pow (cos x) 6))
249.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
206.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
206.0ms
(/ (pow (sin x) 6) (pow (cos x) 6))

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes348.0ms

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
3.0s1529×body1280valid
1.3s1259×body640valid
982.0ms4284×body80valid
501.0ms594×body320valid
141.0ms334×body160valid