Details

Time bar (total: 35.9s)

sample247.0ms

Algorithm
intervals
Results
108.0ms60×body1280valid
34.0ms41×body640valid
19.0ms128×body80valid
7.0ms15×body320valid
5.0ms12×body160valid

simplify90.0ms

Calls
1 calls:
Slowest
89.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×pow1
10×add-cbrt-cube add-exp-log
9×times-frac
8×tan-quot
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative pow-prod-up cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ div-sub div-exp flip-+ div-inv
Calls
4 calls:
Slowest
13.0ms
(* (tan x) (tan x))
11.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
10.0ms
(* (tan x) (tan x))
3.0ms
(- 1 (* (tan x) (tan x)))

series222.0ms

Calls
4 calls:
Slowest
75.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
72.0ms
(* (tan x) (tan x))
42.0ms
(* (tan x) (tan x))
32.0ms
(- 1 (* (tan x) (tan x)))

simplify3.0s

Calls
72 calls:
Slowest
389.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
358.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
353.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
157.0ms
(/ (* (* (- 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)))))
136.0ms
(- 1 (+ (pow x 2) (* 2/3 (pow x 4))))

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
13×add-exp-log
12×associate-*r*
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×add-cbrt-cube
9×associate-*l*
8×tan-quot
4×expm1-log1p-u frac-times associate-*l/ prod-exp associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* pow-prod-down associate-*r/ *-commutative cbrt-unprod
2×pow2 rec-exp flip3-+ pow-plus flip3-- pow-prod-up flip-+ div-inv flip--
1×clear-num frac-2neg un-div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
12.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
10.0ms
(* (tan x) (tan x))
10.0ms
(* (tan x) (tan x))
2.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))

series185.0ms

Calls
4 calls:
Slowest
68.0ms
(* (- 1 (* (tan x) (tan x))) (/ 1 (+ 1 (* (tan x) (tan x)))))
43.0ms
(* (tan x) (tan x))
42.0ms
(* (tan x) (tan x))
32.0ms
(/ 1 (+ 1 (* (tan x) (tan x))))

simplify4.9s

Calls
68 calls:
Slowest
539.0ms
(* (+ (* 1 1) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))) (+ 1 (* (tan x) (tan x))))
471.0ms
(* (- (pow 1 3) (pow (* (tan x) (tan x)) 3)) (/ 1 (+ 1 (* (tan x) (tan x)))))
358.0ms
(* (- (* 1 1) (* (* (tan x) (tan x)) (* (tan x) (tan x)))) (/ 1 (+ 1 (* (tan x) (tan x)))))
352.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
351.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1 times-frac
8×add-cbrt-cube add-exp-log
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×flip3-- flip-- associate-/l/
1×pow2 frac-times cbrt-undiv clear-num sub-neg frac-2neg pow-plus div-sub div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod fma-udef div-inv
Calls
4 calls:
Slowest
7.0ms
(* (tan x) (tan x))
5.0ms
(/ (- 1 (* (tan x) (tan x))) (fma (tan x) (tan x) 1))
1.0ms
(- 1 (* (tan x) (tan x)))
0.0ms
(fma (tan x) (tan x) 1)

series196.0ms

Calls
4 calls:
Slowest
72.0ms
(/ (- 1 (* (tan x) (tan x))) (fma (tan x) (tan x) 1))
53.0ms
(fma (tan x) (tan x) 1)
36.0ms
(- 1 (* (tan x) (tan x)))
35.0ms
(* (tan x) (tan x))

simplify3.0s

Calls
55 calls:
Slowest
441.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
367.0ms
(/ (* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x)))) (* (* (fma (tan x) (tan x) 1) (fma (tan x) (tan x) 1)) (fma (tan x) (tan x) 1)))
357.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
131.0ms
(- (+ (* 2/3 (pow x 4)) 1) (* 2 (pow x 2)))
117.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (/ 1 (fma (tan x) (tan x) 1)) (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1)))
0.3b
(* (tan x) (tan x))
0.2b
(fma (tan x) (tan x) 1)
0.2b
(fma (tan x) (tan x) 1)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
28×prod-diff
26×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
16×div-inv
13×times-frac
9×pow1
6×add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u fma-neg tan-quot insert-posit16 log1p-expm1-u
3×associate-*r* associate-*l*
2×distribute-rgt-out-- fma-udef distribute-lft-out-- difference-of-squares
1×pow2 frac-times sub-neg pow-plus flip3-- diff-log pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up frac-sub cbrt-unprod flip-- sub-div
Calls
4 calls:
Slowest
8.0ms
(- (/ 1 (fma (tan x) (tan x) 1)) (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1)))
5.0ms
(* (tan x) (tan x))
0.0ms
(fma (tan x) (tan x) 1)
0.0ms
(fma (tan x) (tan x) 1)

series231.0ms

Calls
4 calls:
Slowest
132.0ms
(- (/ 1 (fma (tan x) (tan x) 1)) (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1)))
36.0ms
(* (tan x) (tan x))
34.0ms
(fma (tan x) (tan x) 1)
30.0ms
(fma (tan x) (tan x) 1)

simplify13.2s

Calls
100 calls:
Slowest
492.0ms
(fma (* (cbrt (/ 1 (fma (tan x) (tan x) 1))) (cbrt (/ 1 (fma (tan x) (tan x) 1)))) (cbrt (/ 1 (fma (tan x) (tan x) 1))) (- (* (/ 1 (fma (tan x) (tan x) 1)) (* (tan x) (tan x)))))
491.0ms
(fma (- (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1))) 1 (* (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1)) 1))
479.0ms
(fma (* (cbrt (/ 1 (fma (tan x) (tan x) 1))) (cbrt (/ 1 (fma (tan x) (tan x) 1)))) (cbrt (/ 1 (fma (tan x) (tan x) 1))) (- (* (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1)) 1)))
477.0ms
(fma (- (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1))) 1 (* (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1)) 1))
429.0ms
(fma 1 (/ 1 (fma (tan x) (tan x) 1)) (- (* (/ (* (tan x) (tan x)) (fma (tan x) (tan x) 1)) 1)))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.7s1504×body1280valid
1.4s1240×body640valid
1.1s4336×body80valid
391.0ms611×body320valid
130.0ms309×body160valid