Details

Time bar (total: 2.1m)

sample451.0ms

Algorithm
intervals
Results
82.0ms50×body1280valid
48.0ms39×body640valid
32.0ms143×body80valid
11.0ms14×body320valid
5.0ms10×body160valid

simplify261.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
260.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

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

rewrite93.0ms

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
39.0ms
(* (tan x) (tan x))
31.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(- 1 (* (tan x) (tan x)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
55.0ms
(* (tan x) (tan x))
49.0ms
(* (tan x) (tan x))
39.0ms
(- 1 (* (tan x) (tan x)))

simplify10.2s

Counts
170 → 140
Calls
170 calls:
Slowest
563.0ms
(* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x))))
559.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
540.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
422.0ms
(* (* (/ (- 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)))))
357.0ms
(* (+ 1 (* (tan x) (tan x))) (+ (* 1 1) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))))

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
25×add-cube-cbrt
18×prod-diff
13×pow1 add-cbrt-cube add-exp-log
11×distribute-rgt-in distribute-lft-in
9×frac-times associate-*r*
8×flip3-+ flip-+ associate-/l/
7×associate-*l*
6×flip3-- flip-- add-log-exp
5×associate-*l/ associate-*r/
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u
3×associate-/r* fma-def times-frac swap-sqr prod-exp cbrt-unprod
2×cbrt-undiv sub-neg div-exp pow-prod-down associate-/r/ *-commutative distribute-lft-out difference-of-squares unswap-sqr
1×pow2 +-commutative clear-num sum-log frac-2neg pow-plus pow-sqr pow-prod-up div-inv associate-/l* distribute-lft-out--
Counts
4 → 138
Calls
4 calls:
Slowest
26.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
21.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
17.0ms
(* (tan x) (tan x))
5.0ms
(+ 1 (tan x))

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
98.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
47.0ms
(* (tan x) (tan x))
31.0ms
(+ 1 (tan x))

simplify49.6s

Counts
181 → 150
Calls
181 calls:
Slowest
1.0s
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
1.0s
(* (+ 1 (tan x)) (fma (sqrt 1) (sqrt 1) (- (* (sqrt (tan x)) (sqrt (tan x))))))
973.0ms
(* (fma 1 1 (- (* (tan x) 1))) (+ 1 (tan x)))
940.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
925.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
31×*-un-lft-identity
28×add-cube-cbrt
20×pow1
18×prod-diff
15×add-cbrt-cube add-exp-log
12×flip3-- associate-*r* flip--
11×distribute-rgt-in distribute-lft-in
10×frac-times associate-*l*
8×tan-quot associate-/l/
6×swap-sqr associate-*l/ associate-*r/
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac pow-prod-down *-commutative difference-of-squares unswap-sqr
2×pow2 cbrt-undiv sub-neg pow-plus div-exp pow-sqr pow-prod-up
1×clear-num frac-2neg div-inv associate-/l* distribute-lft-out--
Counts
4 → 149
Calls
4 calls:
Slowest
75.0ms
(* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x)))
44.0ms
(/ (* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x))) (fma (* (tan x) (tan x)) (- 1 (tan x)) (- 1 (tan x))))
18.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
254.0ms
(/ (* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x))) (fma (* (tan x) (tan x)) (- 1 (tan x)) (- 1 (tan x))))
57.0ms
(* (- (* 1 1) (* (tan x) (tan x))) (- 1 (tan x)))
50.0ms
(* (tan x) (tan x))
44.0ms
(* (tan x) (tan x))

simplify41.3s

Counts
197 → 161
Calls
197 calls:
Slowest
1.4s
(* (fma (* (tan x) (tan x)) (- 1 (tan x)) (- 1 (tan x))) (+ (* (* 1 1) (* 1 1)) (+ (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (* 1 1) (* (tan x) (tan x))))))
1.2s
(* (fma (* (tan x) (tan x)) (- 1 (tan x)) (- 1 (tan x))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
1.1s
(* (fma (* (tan x) (tan x)) (- 1 (tan x)) (- 1 (tan x))) (* (+ (* 1 1) (* (tan x) (tan x))) (+ 1 (tan x))))
984.0ms
(* (fma 1 1 (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x)))))) (- (* 1 1) (* (tan x) (tan x))))
841.0ms
(/ (- 1 (tan x)) (cbrt (fma (* (tan x) (tan x)) (- 1 (tan x)) (- 1 (tan x)))))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity add-cube-cbrt
12×times-frac
11×pow1
8×add-cbrt-cube add-exp-log
6×add-log-exp
5×difference-of-squares
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* swap-sqr associate-*r* associate-*l*
2×flip3-- flip-- associate-/l/
1×pow2 frac-times cbrt-undiv clear-num sub-neg frac-2neg pow-plus fma-neg diff-log div-sub div-exp prod-diff pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef div-inv unswap-sqr
Counts
4 → 97
Calls
4 calls:
Slowest
26.0ms
(/ (- (* 1 1) (* (tan x) (tan x))) (fma (tan x) (tan x) 1))
14.0ms
(* (tan x) (tan x))
9.0ms
(- (* 1 1) (* (tan x) (tan x)))
0.0ms
(fma (tan x) (tan x) 1)

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(/ (- (* 1 1) (* (tan x) (tan x))) (fma (tan x) (tan x) 1))
70.0ms
(fma (tan x) (tan x) 1)
58.0ms
(- (* 1 1) (* (tan x) (tan x)))
54.0ms
(* (tan x) (tan x))

simplify9.3s

Counts
130 → 109
Calls
130 calls:
Slowest
588.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
587.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
491.0ms
(* (* (- (* 1 1) (* (tan x) (tan x))) (- (* 1 1) (* (tan x) (tan x)))) (- (* 1 1) (* (tan x) (tan x))))
435.0ms
(/ (* (* (- (* 1 1) (* (tan x) (tan x))) (- (* 1 1) (* (tan x) (tan x)))) (- (* 1 1) (* (tan x) (tan x)))) (* (* (fma (tan x) (tan x) 1) (fma (tan x) (tan x) 1)) (fma (tan x) (tan x) 1)))
387.0ms
(* (* (/ (- (* 1 1) (* (tan x) (tan x))) (fma (tan x) (tan x) 1)) (/ (- (* 1 1) (* (tan x) (tan x))) (fma (tan x) (tan x) 1))) (/ (- (* 1 1) (* (tan x) (tan x))) (fma (tan x) (tan x) 1)))

prune941.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes198.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.4s1517×body1280valid
1.8s1227×body640valid
946.0ms4317×body80valid
477.0ms605×body320valid
171.0ms334×body160valid