Details

Time bar (total: 1.9m)

sample1.1s

Algorithm
intervals
Results
697.0ms48×body640valid
101.0ms51×body1280valid
59.0ms122×body80valid
21.0ms28×body320valid
4.0ms7×body160valid

simplify71.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
70.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

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

rewrite58.0ms

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
21.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
16.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (* (tan x) (tan x)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
94.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
50.0ms
(* (tan x) (tan x))
45.0ms
(- 1 (* (tan x) (tan x)))
41.0ms
(* (tan x) (tan x))

simplify5.7s

Counts
119 → 140
Calls
119 calls:
Slowest
582.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
457.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
366.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
297.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
295.0ms
(- 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

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
62×*-un-lft-identity
37×times-frac
34×add-cube-cbrt
22×associate-*r*
16×difference-of-squares
11×add-cbrt-cube add-exp-log
9×prod-diff
8×distribute-lft-out-- add-log-exp
6×pow1 associate-/l*
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×associate-/r* fma-def flip3-+ fma-neg flip-+
2×frac-times cbrt-undiv flip3-- div-exp associate-*l/ prod-exp cbrt-unprod div-inv flip-- distribute-lft-out unswap-sqr associate-/l/
1×+-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub pow-prod-down associate-*r/ *-commutative
Counts
4 → 142
Calls
4 calls:
Slowest
52.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
13.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
5.0ms
(- 1 (tan x))
5.0ms
(+ 1 (tan x))

series340.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
95.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
36.0ms
(- 1 (tan x))
32.0ms
(+ 1 (tan x))

simplify8.7s

Counts
130 → 154
Calls
130 calls:
Slowest
599.0ms
(* (- (* 1 1) (* (tan x) (tan x))) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
482.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
391.0ms
(* (+ (pow 1 3) (pow (tan x) 3)) (- 1 (tan x)))
322.0ms
(- 1 (+ x (* 1/3 (pow x 3))))
322.0ms
(/ (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))) (* (* (fma (tan x) (tan x) 1) (fma (tan x) (tan x) 1)) (fma (tan x) (tan x) 1)))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
143×times-frac
136×add-sqr-sqrt
135×prod-diff
124×*-un-lft-identity
116×add-cube-cbrt
54×associate-/r/
30×div-inv
27×flip3-+ flip-+
25×pow1
15×fma-neg
12×tan-quot
10×add-cbrt-cube add-exp-log
9×swap-sqr associate-*r* associate-*l*
6×add-log-exp difference-of-squares
5×distribute-rgt-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
2×distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 273
Calls
4 calls:
Slowest
72.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
20.0ms
(* (tan x) (tan x))
18.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series333.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
62.0ms
(* (tan x) (tan x))
58.0ms
(* (tan x) (tan x))
36.0ms
(* (tan x) (tan x))

simplify1.2m

Counts
399 → 285
Calls
399 calls:
Slowest
829.0ms
(fma (- (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x))))) 1 (* (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))) 1))
733.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (+ 1 (* (tan x) (tan x))))) (/ (cbrt 1) (sqrt (+ 1 (* (tan x) (tan x))))) (- (* (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))) 1)))
655.0ms
(- (* 1 (+ 1 (* (tan x) (tan x)))) (* (+ 1 (* (tan x) (tan x))) (* (tan x) (tan x))))
585.0ms
(fma (* (cbrt (/ 1 (+ 1 (* (tan x) (tan x))))) (cbrt (/ 1 (+ 1 (* (tan x) (tan x)))))) (cbrt (/ 1 (+ 1 (* (tan x) (tan x))))) (- (* (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))) 1)))
574.0ms
(fma 1 (/ 1 (+ 1 (* (tan x) (tan x)))) (- (* (/ 1 (+ 1 (* (tan x) (tan x)))) (* (tan x) (tan x)))))

prune2.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
26×add-cube-cbrt
21×prod-diff
13×pow1 add-cbrt-cube add-exp-log
12×times-frac
6×associate-*r* associate-*l* tan-quot add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×associate-/r* fma-neg swap-sqr prod-exp associate-*r/ cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative difference-of-squares unswap-sqr
1×pow2 frac-times clear-num sub-neg frac-2neg pow-plus flip3-- diff-log associate-*l/ pow-sqr pow-prod-up flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 120
Calls
4 calls:
Slowest
29.0ms
(/ (* (sin x) (tan x)) (cos x))
20.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))
17.0ms
(* (sin x) (tan x))
16.0ms
(* (tan x) (tan x))

series309.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))
83.0ms
(/ (* (sin x) (tan x)) (cos x))
82.0ms
(* (sin x) (tan x))
58.0ms
(* (tan x) (tan x))

simplify12.1s

Counts
113 → 132
Calls
113 calls:
Slowest
675.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
342.0ms
(fma (sqrt 1) (sqrt 1) (- (* (/ (tan x) (cbrt (cos x))) (/ (sin x) (* (cbrt (cos x)) (cbrt (cos x)))))))
329.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
311.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (tan x) (tan x)) (tan x)))
306.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (/ (tan x) (cbrt (cos x))) (/ (sin x) (* (cbrt (cos x)) (cbrt (cos x)))))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes198.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.4s1555×body1280valid
1.7s1232×body640valid
999.0ms4281×body80valid
434.0ms613×body320valid
173.0ms319×body160valid