Details

Time bar (total: 55.0s)

sample299.0ms

Algorithm
intervals
Results
131.0ms59×body1280valid
44.0ms41×body640valid
28.0ms128×body80valid
13.0ms19×body320valid
4.0ms9×body160valid

simplify131.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
130.0ms
(/ (- 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

localize17.0ms

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

rewrite63.0ms

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
27.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
4.0ms
(- 1 (* (tan x) (tan x)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
65.0ms
(* (tan x) (tan x))
57.0ms
(- 1 (* (tan x) (tan x)))
35.0ms
(* (tan x) (tan x))

simplify6.2s

Counts
111 → 126
Calls
111 calls:
Slowest
637.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
572.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
511.0ms
(/ (* (* (- 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)))))
391.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
326.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.2b
(/ (sin x) (cos x))
0.2b
(/ (sin x) (cos x))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
100×add-sqr-sqrt
98×times-frac
76×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
18×pow1
10×cbrt-undiv div-exp div-inv
8×prod-exp cbrt-unprod unswap-sqr
6×associate-/r* associate-/l*
4×insert-posit16 add-log-exp
2×pow2 frac-times quot-tan clear-num frac-2neg pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 194
Calls
4 calls:
Slowest
36.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
19.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
11.0ms
(/ (sin x) (cos x))
8.0ms
(/ (sin x) (cos x))

series216.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
76.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
35.0ms
(/ (sin x) (cos x))
23.0ms
(/ (sin x) (cos x))

simplify8.7s

Counts
216 → 206
Calls
216 calls:
Slowest
532.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))
446.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
424.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))
408.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
262.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.2b
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
87×add-sqr-sqrt
83×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
21×associate-/r*
19×pow1 add-exp-log
13×add-cbrt-cube
9×associate-/r/
8×tan-quot
7×div-exp
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×flip3-- div-inv flip--
4×insert-posit16
3×cbrt-undiv associate-/l*
2×pow2 frac-times rec-exp pow-plus 1-exp pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×clear-num sub-neg frac-2neg diff-log pow-flip inv-pow
Counts
4 → 182
Calls
4 calls:
Slowest
30.0ms
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
15.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))
9.0ms
(- 1 (* (tan x) (tan x)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
57.0ms
(- 1 (* (tan x) (tan x)))
51.0ms
(* (tan x) (tan x))
41.0ms
(* (tan x) (tan x))

simplify17.0s

Counts
224 → 194
Calls
224 calls:
Slowest
600.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
541.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
541.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
382.0ms
(/ (sqrt 1) (/ (* (cbrt (+ 1 (* (tan x) (tan x)))) (cbrt (+ 1 (* (tan x) (tan x))))) (* (cbrt (- 1 (* (tan x) (tan x)))) (cbrt (- 1 (* (tan x) (tan x)))))))
367.0ms
(/ (* (* 1 1) 1) (* (* (/ (+ 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))))))

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.2b
(* (sin x) (/ (/ (sin x) (cos x)) (cos x)))
0.2b
(/ (sin x) (cos x))
0.2b
(/ (sin x) (cos x))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
105×add-sqr-sqrt
84×*-un-lft-identity add-cube-cbrt
56×associate-*r*
29×add-cbrt-cube add-exp-log
16×associate-*l*
13×pow1 swap-sqr
10×div-inv
9×cbrt-undiv div-exp
7×prod-exp cbrt-unprod unswap-sqr
6×associate-/r* associate-/l*
4×insert-posit16 add-log-exp
2×quot-tan clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
1×pow2 frac-times pow-plus associate-*l/ pow-sqr pow-prod-up
Counts
4 → 192
Calls
4 calls:
Slowest
42.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
22.0ms
(* (sin x) (/ (/ (sin x) (cos x)) (cos x)))
13.0ms
(/ (sin x) (cos x))
8.0ms
(/ (sin x) (cos x))

series181.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(* (sin x) (/ (/ (sin x) (cos x)) (cos x)))
62.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
23.0ms
(/ (sin x) (cos x))
22.0ms
(/ (sin x) (cos x))

simplify7.8s

Counts
198 → 204
Calls
198 calls:
Slowest
536.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (/ (sin x) (cos x)) (cos x)) (/ (/ (sin x) (cos x)) (cos x))) (/ (/ (sin x) (cos x)) (cos x))))
459.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))
391.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
349.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
295.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes425.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end1.0ms

sample5.9s

Algorithm
intervals
Results
2.0s1445×body1280valid
1.4s4294×body80valid
1.3s1280×body640valid
944.0ms645×body320valid
134.0ms336×body160valid