Details

Time bar (total: 17.6s)

sample516.0ms

Algorithm
intervals
Results
182.0ms50×body1280valid
62.0ms39×body640valid
36.0ms143×body80valid
13.0ms14×body320valid
6.0ms10×body160valid

simplify77.0ms

Counts
1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

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
29.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
26.0ms
(* (tan x) (tan x))
17.0ms
(- 1 (* (tan x) (tan x)))
17.0ms
(* (tan x) (tan x))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
73.0ms
(* (tan x) (tan x))
59.0ms
(- 1 (* (tan x) (tan x)))
57.0ms
(* (tan x) (tan x))

simplify482.0ms

Counts
170 → 140

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
136×pow1
44×tan-quot
39×pow-prod-up
26×pow-prod-down
25×pow-sqr
22×add-sqr-sqrt add-cbrt-cube add-exp-log
21×pow-plus
20×frac-times
16×pow2 *-un-lft-identity add-cube-cbrt
14×associate-*l/ associate-*r/
11×prod-exp cbrt-unprod
10×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
Counts
4 → 174
Calls
4 calls:
Slowest
106.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
28.0ms
(* (tan x) (tan x))
17.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
63.0ms
(* (tan x) (tan x))
58.0ms
(* (tan x) (tan x))
56.0ms
(* (tan x) (tan x))

simplify845.0ms

Counts
204 → 186

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 202
Calls
4 calls:
Slowest
37.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
36.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
11.0ms
(/ (sin x) (cos x))
8.0ms
(/ (sin x) (cos x))

series202.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
47.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
37.0ms
(/ (sin x) (cos x))
37.0ms
(/ (sin x) (cos x))

simplify527.0ms

Counts
264 → 214

prune2.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
39×*-un-lft-identity
32×add-cube-cbrt
30×times-frac
22×log-pow
21×exp-prod
19×pow1
14×difference-of-squares
10×add-cbrt-cube add-exp-log
8×tan-quot
6×swap-sqr associate-*r* associate-*l*
5×associate-/l*
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/r*
2×pow2 frac-times flip3-+ pow-plus div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv unswap-sqr associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-- exp-diff div-exp rem-log-exp flip--
Counts
4 → 142
Calls
4 calls:
Slowest
30.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
25.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
18.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
104.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
42.0ms
(* (tan x) (tan x))
39.0ms
(* (tan x) (tan x))

simplify913.0ms

Counts
180 → 154

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.3s1517×body1280valid
1.7s1227×body640valid
874.0ms4317×body80valid
431.0ms605×body320valid
192.0ms334×body160valid