Details

Time bar (total: 34.7s)

sample239.0ms

Algorithm
intervals
Results
69.0ms59×body1280valid
48.0ms9×body160valid
31.0ms41×body640valid
23.0ms128×body80valid
13.0ms19×body320valid

simplify135.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
134.0ms
(/ (- 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))))

rewrite88.0ms

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
36.0ms
(* (tan x) (tan x))
29.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
6.0ms
(- 1 (* (tan x) (tan x)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
76.0ms
(* (tan x) (tan x))
53.0ms
(* (tan x) (tan x))
47.0ms
(- 1 (* (tan x) (tan x)))

simplify5.9s

Counts
119 → 140
Calls
119 calls:
Slowest
594.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
460.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
355.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
346.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
302.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
67×times-frac
56×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
9×associate-/r* associate-/l*
7×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×quot-tan clear-num frac-2neg
1×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 163
Calls
4 calls:
Slowest
20.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
14.0ms
(/ (sin x) (cos x))
10.0ms
(/ (sin x) (cos x))
8.0ms
(/ (sin x) (cos x))

series167.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
57.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
42.0ms
(/ (sin x) (cos x))
36.0ms
(/ (sin x) (cos x))
32.0ms
(/ (sin x) (cos x))

simplify7.0s

Counts
164 → 175
Calls
164 calls:
Slowest
503.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
488.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))
465.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
463.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
347.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
37×times-frac
36×*-un-lft-identity add-cube-cbrt
15×add-cbrt-cube add-exp-log
13×associate-*l*
9×associate-/r* associate-/l*
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
3×quot-tan clear-num frac-2neg associate-*r*
2×prod-exp tan-quot cbrt-unprod unswap-sqr
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 130
Calls
4 calls:
Slowest
22.0ms
(/ (sin x) (cos x))
17.0ms
(* (/ (sin x) (cos x)) (tan x))
16.0ms
(/ (sin x) (cos x))
8.0ms
(/ (sin x) (cos x))

series212.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
95.0ms
(* (/ (sin x) (cos x)) (tan x))
43.0ms
(/ (sin x) (cos x))
37.0ms
(/ (sin x) (cos x))
37.0ms
(/ (sin x) (cos x))

simplify4.1s

Counts
115 → 142
Calls
115 calls:
Slowest
446.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
412.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
403.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
318.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))
307.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

3.3b
(log (exp (/ (sin x) (cos x))))
0.3b
(* (/ (sin x) (cos x)) (tan x))
0.3b
(exp (/ (sin x) (cos x)))
0.2b
(/ (sin x) (cos x))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
37×times-frac
35×*-un-lft-identity add-cube-cbrt
26×exp-prod
14×log-pow
13×associate-*l*
11×add-cbrt-cube add-exp-log
7×pow1
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×log-prod associate-/r* associate-*r* associate-/l*
2×cbrt-undiv div-exp prod-exp tan-quot cbrt-unprod unswap-sqr
1×frac-times quot-tan clear-num frac-2neg rem-log-exp pow-prod-down associate-*l/ associate-*r/ *-commutative rem-exp-log
Counts
4 → 120
Calls
4 calls:
Slowest
22.0ms
(* (/ (sin x) (cos x)) (tan x))
16.0ms
(/ (sin x) (cos x))
13.0ms
(exp (/ (sin x) (cos x)))
9.0ms
(log (exp (/ (sin x) (cos x))))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(* (/ (sin x) (cos x)) (tan x))
65.0ms
(exp (/ (sin x) (cos x)))
33.0ms
(log (exp (/ (sin x) (cos x))))
22.0ms
(/ (sin x) (cos x))

simplify3.3s

Counts
96 → 132
Calls
96 calls:
Slowest
404.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
312.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))
309.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))
264.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
260.0ms
(* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (tan x) (tan x)) (tan x)))

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes433.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.1s1445×body1280valid
1.8s1280×body640valid
1.3s4294×body80valid
434.0ms645×body320valid
168.0ms336×body160valid