Details

Time bar (total: 15.4s)

sample412.0ms

Algorithm
intervals
Results
58.0ms37×body640valid
52.0ms45×body1280valid
51.0ms135×body80valid
14.0ms28×body320valid
4.0ms11×body160valid

simplify69.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b
(- 1.0 (* (tan x) (tan x)))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×pow1
12×times-frac
10×add-exp-log add-cbrt-cube
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×associate-/l*
3×associate-/r*
2×pow2 frac-times flip3-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
61.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
12.0ms
(- 1.0 (* (tan x) (tan x)))
37.0ms
(* (tan x) (tan x))
42.0ms
(* (tan x) (tan x))

series343.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
45.0ms
(- 1.0 (* (tan x) (tan x)))
80.0ms
(* (tan x) (tan x))
83.0ms
(* (tan x) (tan x))

simplify558.0ms

Counts
117 → 117

prune431.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (cos x) 2)
0.2b
(pow (cos x) 2)
0.3b
(pow (sin x) 2)
0.3b
(pow (sin x) 2)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down pow-unpow *-un-lft-identity
8×pow1 add-exp-log
4×pow-to-exp pow-pow pow-exp add-cbrt-cube unpow2 add-log-exp sqr-pow
Counts
4 → 72
Calls
4 calls:
4.0ms
(pow (cos x) 2)
4.0ms
(pow (cos x) 2)
4.0ms
(pow (sin x) 2)
4.0ms
(pow (sin x) 2)

series86.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(pow (cos x) 2)
24.0ms
(pow (cos x) 2)
19.0ms
(pow (sin x) 2)
20.0ms
(pow (sin x) 2)

simplify884.0ms

Counts
84 → 84

prune354.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.3b
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
25×pow1
18×*-un-lft-identity
16×add-cube-cbrt
12×tan-quot
10×add-exp-log add-cbrt-cube
9×swap-sqr associate-*r* associate-*l*
6×add-log-exp
4×times-frac associate-/r/ difference-of-squares
3×pow2 frac-times distribute-rgt-out-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
2×flip3-+ flip-+ div-inv
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
4 → 106
Calls
4 calls:
33.0ms
(* (tan x) (tan x))
33.0ms
(* (tan x) (tan x))
33.0ms
(* (tan x) (tan x))
117.0ms
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series441.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (tan x) (tan x))
38.0ms
(* (tan x) (tan x))
61.0ms
(* (tan x) (tan x))
291.0ms
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify2.4s

Counts
118 → 118

prune349.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.3b
(- (/ 1.0 (- (* 1.0 1.0) (* (* (tan x) (tan x)) (* (tan x) (tan x))))) (/ (* (tan x) (tan x)) (- (* 1.0 1.0) (* (* (tan x) (tan x)) (* (tan x) (tan x))))))
0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite409.0ms

Algorithm
rewrite-expression-head
Rules
233×pow1
73×pow-prod-up
68×tan-quot
47×pow-prod-down
45×pow-sqr
37×pow-plus
35×frac-times
30×add-exp-log add-cbrt-cube
27×pow2
23×associate-*r/ associate-*l/
20×add-sqr-sqrt
17×prod-exp cbrt-unprod
10×*-un-lft-identity
8×add-cube-cbrt
6×add-log-exp
5×swap-sqr associate-*r* associate-*l*
4×times-frac associate-/r/ difference-of-squares
3×flip3-- distribute-rgt-out-- *-commutative flip-- unswap-sqr
2×div-inv
1×sub-neg diff-log frac-sub distribute-lft-out-- sub-div
Counts
4 → 206
Calls
4 calls:
22.0ms
(* (tan x) (tan x))
145.0ms
(- (/ 1.0 (- (* 1.0 1.0) (* (* (tan x) (tan x)) (* (tan x) (tan x))))) (/ (* (tan x) (tan x)) (- (* 1.0 1.0) (* (* (tan x) (tan x)) (* (tan x) (tan x))))))
121.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
99.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (tan x) (tan x))
297.0ms
(- (/ 1.0 (- (* 1.0 1.0) (* (* (tan x) (tan x)) (* (tan x) (tan x))))) (/ (* (tan x) (tan x)) (- (* 1.0 1.0) (* (* (tan x) (tan x)) (* (tan x) (tan x))))))
79.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
63.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify785.0ms

Counts
218 → 218

prune466.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes422.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.3s

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.0s1502×body1280valid
1.1s4251×body80valid
856.0ms1255×body640valid
359.0ms670×body320valid
84.0ms322×body160valid