Details

Time bar (total: 1.1m)

sample491.0ms

Algorithm
intervals
Results
212.0ms143×body80valid
83.0ms47×body1280valid
58.0ms44×body640valid
17.0ms16×body320valid
4.0ms6×body160valid

simplify107.0ms

Calls
1 calls:
Slowest
105.0ms
(/ (- 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

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.1b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×pow1
10×add-cbrt-cube add-exp-log
9×times-frac
8×tan-quot
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative pow-prod-up cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ div-sub div-exp flip-+ div-inv
Calls
4 calls:
Slowest
15.0ms
(* (tan x) (tan x))
7.0ms
(* (tan x) (tan x))
5.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
1.0ms
(- 1 (* (tan x) (tan x)))

series178.0ms

Calls
4 calls:
Slowest
61.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
49.0ms
(* (tan x) (tan x))
41.0ms
(* (tan x) (tan x))
27.0ms
(- 1 (* (tan x) (tan x)))

simplify3.1s

Calls
72 calls:
Slowest
359.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
330.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
322.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
150.0ms
(/ (* (* (- 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)))))
139.0ms
(- 1 (+ (pow x 2) (* 2/3 (pow x 4))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
76×pow1
44×tan-quot
26×pow-prod-up
22×add-cbrt-cube add-exp-log
21×pow-prod-down
20×frac-times
15×pow-plus
14×associate-*l/ associate-*r/
12×pow2
11×prod-exp cbrt-unprod
10×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
Calls
4 calls:
Slowest
34.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))

series142.0ms

Calls
4 calls:
Slowest
47.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
36.0ms
(* (tan x) (tan x))
34.0ms
(* (tan x) (tan x))
25.0ms
(* (tan x) (tan x))

simplify2.1s

Calls
132 calls:
Slowest
164.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
148.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
124.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
123.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
65.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

12.4b
(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
0.3b
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
392×tan-quot
286×pow1
260×frac-times
176×associate-*l/
166×pow-prod-up
112×associate-*r/
111×pow-plus
72×pow-prod-down
63×cbrt-div
44×add-cbrt-cube add-exp-log
39×pow2
29×prod-exp cbrt-unprod
18×pow3
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
1×cbrt-prod pow1/3 rem-cbrt-cube
Calls
4 calls:
Slowest
83.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
72.0ms
(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
10.0ms
(* (tan x) (tan x))
9.0ms
(* (tan x) (tan x))

series150.0ms

Calls
4 calls:
Slowest
43.0ms
(* (tan x) (tan x))
42.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
35.0ms
(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
30.0ms
(* (tan x) (tan x))

simplify20.6s

Calls
408 calls:
Slowest
767.0ms
(* (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (tan x) (tan x)) (tan x))))
445.0ms
(* (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))))
420.0ms
(* (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))))
406.0ms
(* (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (tan x) (tan x)) (tan x))))
386.0ms
(* (* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (tan x) (tan x)) (tan x))))

prune3.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (/ 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))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
54×prod-diff
36×add-sqr-sqrt *-un-lft-identity associate-/r/
32×add-cube-cbrt
20×div-inv
19×pow1 times-frac
18×flip3-+ flip-+
12×tan-quot
10×add-cbrt-cube add-exp-log
9×associate-*r* associate-*l*
6×fma-neg add-log-exp
4×expm1-log1p-u distribute-rgt-out-- insert-posit16 log1p-expm1-u
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod
2×distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Calls
4 calls:
Slowest
9.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
6.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))

series236.0ms

Calls
4 calls:
Slowest
109.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
46.0ms
(* (tan x) (tan x))
43.0ms
(* (tan x) (tan x))
38.0ms
(* (tan x) (tan x))

simplify26.9s

Calls
188 calls:
Slowest
714.0ms
(- (* 1 (+ 1 (* (tan x) (tan x)))) (* (+ 1 (* (tan x) (tan x))) (* (tan x) (tan x))))
557.0ms
(fma 1 (/ 1 (+ 1 (* (tan x) (tan x)))) (- (* (/ 1 (+ 1 (* (tan x) (tan x)))) (* (tan x) (tan x)))))
549.0ms
(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)))
528.0ms
(fma 1 (/ 1 (+ 1 (* (tan x) (tan x)))) (- (* (/ 1 (+ 1 (* (tan x) (tan x)))) (* (tan x) (tan x)))))
513.0ms
(fma (- (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x))))) 1 (* (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))) 1))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes263.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.2s1506×body1280valid
1.3s1246×body640valid
826.0ms4295×body80valid
506.0ms307×body160valid
374.0ms646×body320valid