Details

Time bar (total: 43.5s)

sample296.0ms

Algorithm
intervals
Results
60.0ms46×body1280valid
35.0ms39×body640valid
33.0ms139×body80valid
14.0ms22×body320valid
4.0ms10×body160valid

simplify58.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
57.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

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))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
27×*-un-lft-identity
22×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×insert-posit16
3×associate-/r*
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 → 114
Calls
4 calls:
Slowest
18.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))
15.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
4.0ms
(- 1 (* (tan x) (tan x)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
59.0ms
(- 1 (* (tan x) (tan x)))
49.0ms
(* (tan x) (tan x))
36.0ms
(* (tan x) (tan x))

simplify6.5s

Counts
111 → 126
Calls
111 calls:
Slowest
643.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
592.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
519.0ms
(/ (* (* (- 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)))))
504.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
364.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
13×pow1
10×add-cube-cbrt
9×associate-*r*
8×add-cbrt-cube add-exp-log add-log-exp
7×associate-*l*
5×frac-times
4×flip3-+ flip3-- tan-quot flip-+ insert-posit16 flip-- difference-of-squares
3×sub-neg swap-sqr associate-*l/ associate-*r/
2×distribute-rgt-in distribute-lft-in 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 → 93
Calls
4 calls:
Slowest
23.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
13.0ms
(* (tan x) (tan x))
4.0ms
(+ 1 (tan x))
4.0ms
(- 1 (tan x))

series170.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
44.0ms
(* (tan x) (tan x))
26.0ms
(+ 1 (tan x))
24.0ms
(- 1 (tan x))

simplify7.0s

Counts
74 → 105
Calls
74 calls:
Slowest
757.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
669.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
451.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
429.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
405.0ms
(* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x)))

prune866.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
13×pow1
10×add-cube-cbrt
9×associate-*r*
8×add-cbrt-cube add-exp-log add-log-exp
7×associate-*l*
5×frac-times
4×flip3-+ flip3-- tan-quot flip-+ insert-posit16 flip-- difference-of-squares
3×sub-neg swap-sqr associate-*l/ associate-*r/
2×distribute-rgt-in distribute-lft-in 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 → 93
Calls
4 calls:
Slowest
29.0ms
(* (+ (tan x) 1) (- 1 (tan x)))
29.0ms
(* (tan x) (tan x))
10.0ms
(+ (tan x) 1)
9.0ms
(- 1 (tan x))

series175.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(* (+ (tan x) 1) (- 1 (tan x)))
37.0ms
(* (tan x) (tan x))
32.0ms
(+ (tan x) 1)
31.0ms
(- 1 (tan x))

simplify6.7s

Counts
74 → 105
Calls
74 calls:
Slowest
887.0ms
(* (+ (* (tan x) (tan x)) (- (* 1 1) (* (tan x) 1))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
674.0ms
(* (* (* (+ (tan x) 1) (+ (tan x) 1)) (+ (tan x) 1)) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
443.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
410.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
393.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
17×associate-*l/
16×add-sqr-sqrt *-un-lft-identity
13×pow1 flip3-+ associate-*r* tan-quot flip-+
12×add-cube-cbrt
10×frac-add
9×distribute-neg-frac
8×add-cbrt-cube add-exp-log add-log-exp
7×frac-times associate-*l*
4×associate-*r/ insert-posit16
3×distribute-lft-neg-in distribute-rgt-neg-in swap-sqr distribute-rgt-neg-out distribute-lft-out
2×+-commutative sum-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×pow2 neg-mul-1 pow-plus unsub-neg pow-sqr pow-prod-up
Counts
4 → 100
Calls
4 calls:
Slowest
33.0ms
(* (+ 1 (tan x)) (- (tan x)))
30.0ms
(+ (* (+ 1 (tan x)) 1) (* (+ 1 (tan x)) (- (tan x))))
25.0ms
(* (tan x) (tan x))
4.0ms
(+ 1 (tan x))

series166.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
58.0ms
(* (+ 1 (tan x)) (- (tan x)))
43.0ms
(* (tan x) (tan x))
35.0ms
(+ (* (+ 1 (tan x)) 1) (* (+ 1 (tan x)) (- (tan x))))
30.0ms
(+ 1 (tan x))

simplify11.3s

Counts
88 → 112
Calls
88 calls:
Slowest
685.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (- 1 (tan x)))
672.0ms
(* (exp (* (+ 1 (tan x)) 1)) (exp (* (+ 1 (tan x)) (- (tan x)))))
601.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- (tan x)) (- (tan x))) (- (tan x))))
554.0ms
(+ (* (* (- (* 1 1) (* (tan x) (tan x))) 1) (* (- 1 (tan x)) (cos x))) (* (- 1 (tan x)) (* (- (* 1 1) (* (tan x) (tan x))) (- (sin x)))))
534.0ms
(* (- 1 (tan x)) (* (- 1 (tan x)) (cos x)))

prune967.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes213.0ms

Accuracy

0% (0.3b remaining)

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

bsearch7.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.3s1529×body1280valid
1.4s1259×body640valid
1.3s4284×body80valid
744.0ms594×body320valid
139.0ms334×body160valid