Details

Time bar (total: 43.5s)

sample397.0ms

Algorithm
intervals
Results
198.0ms50×body1280valid
75.0ms41×body640valid
27.0ms136×body80valid
19.0ms22×body320valid
3.0ms7×body160valid

simplify126.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
125.0ms
(/ (- 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

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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
26.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
4.0ms
(- 1 (* (tan x) (tan x)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
50.0ms
(* (tan x) (tan x))
47.0ms
(- 1 (* (tan x) (tan x)))
33.0ms
(* (tan x) (tan x))

simplify6.3s

Counts
111 → 126
Calls
111 calls:
Slowest
602.0ms
(/ (* (* (- 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)))))
572.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
571.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
451.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
353.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
55×*-un-lft-identity
37×times-frac
30×add-cube-cbrt
27×associate-*r*
14×difference-of-squares
13×pow1 add-cbrt-cube add-exp-log
7×associate-*l* distribute-lft-out--
6×associate-/l* add-log-exp
5×flip3-+ flip-+
4×tan-quot associate-/r/ insert-posit16
3×frac-times associate-/r* swap-sqr associate-*l/ prod-exp cbrt-unprod unswap-sqr
2×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative div-inv distribute-lft-out associate-/l/
1×pow2 +-commutative clear-num sum-log frac-2neg pow-plus flip3-- div-sub pow-sqr pow-prod-up flip--
Counts
4 → 136
Calls
4 calls:
Slowest
65.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
27.0ms
(* (tan x) (tan x))
24.0ms
(/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x))))
9.0ms
(+ 1 (tan x))

series302.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
78.0ms
(/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x))))
36.0ms
(* (tan x) (tan x))
30.0ms
(+ 1 (tan x))

simplify10.1s

Counts
131 → 148
Calls
131 calls:
Slowest
628.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
554.0ms
(* (+ (pow 1 3) (pow (tan x) 3)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
536.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
510.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
470.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

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
31.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
14.0ms
(* (tan x) (tan x))
11.0ms
(+ 1 (tan x))
8.0ms
(- 1 (tan x))

series160.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
59.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
45.0ms
(* (tan x) (tan x))
30.0ms
(+ 1 (tan x))
26.0ms
(- 1 (tan x))

simplify6.7s

Counts
74 → 105
Calls
74 calls:
Slowest
817.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
621.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
393.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
389.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
369.0ms
(* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x)))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
27×*-un-lft-identity
18×exp-prod
16×add-cube-cbrt
15×pow1 log-prod
14×log-pow
13×associate-*r*
8×add-cbrt-cube exp-sum add-exp-log
7×associate-*l* add-log-exp
6×difference-of-squares
5×distribute-rgt-in distribute-lft-in
4×sub-neg tan-quot insert-posit16
3×swap-sqr associate-*l/ distribute-lft-out--
2×exp-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
1×pow2 frac-times log-div flip3-+ pow-plus diff-log rem-log-exp associate-*r/ pow-sqr pow-prod-up flip-+ distribute-lft-out
Counts
4 → 109
Calls
4 calls:
Slowest
70.0ms
(* (+ 1 (tan x)) (log (exp (- 1 (tan x)))))
21.0ms
(exp (- 1 (tan x)))
20.0ms
(log (exp (- 1 (tan x))))
15.0ms
(* (tan x) (tan x))

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(* (+ 1 (tan x)) (log (exp (- 1 (tan x)))))
58.0ms
(exp (- 1 (tan x)))
51.0ms
(* (tan x) (tan x))
27.0ms
(log (exp (- 1 (tan x))))

simplify6.8s

Counts
89 → 121
Calls
89 calls:
Slowest
800.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (log (exp (- 1 (tan x)))) (log (exp (- 1 (tan x))))) (log (exp (- 1 (tan x))))))
481.0ms
(* (log (exp (- 1 (tan x)))) (+ 1 (tan x)))
462.0ms
(* (- (* 1 1) (* (tan x) (tan x))) (log (exp (- 1 (tan x)))))
434.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
405.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes375.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.8s1522×body1280valid
1.5s1249×body640valid
1.2s4325×body80valid
419.0ms604×body320valid
128.0ms300×body160valid