Details

Time bar (total: 21.2s)

sample656.0ms

Algorithm
intervals
Results
151.0ms44×body640valid
148.0ms45×body1280valid
38.0ms138×body80valid
17.0ms20×body320valid
5.0ms9×body160valid

simplify32.0ms

Counts
1 → 1
Iterations
IterNodes
done44
544
439
331
224
115
07

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b
(- 1 (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite55.0ms

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:
15.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(- 1 (* (tan x) (tan x)))
15.0ms
(* (tan x) (tan x))
16.0ms
(* (tan x) (tan x))

series404.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
52.0ms
(- 1 (* (tan x) (tan x)))
105.0ms
(* (tan x) (tan x))
151.0ms
(* (tan x) (tan x))

simplify2.9s

Counts
140 → 140
Iterations
IterNodes
done5126
33513
21102
1401
0157

prune661.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1 (* (tan x) (tan x)))
0.3b
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×pow1
15×*-un-lft-identity
14×add-cube-cbrt
8×add-cbrt-cube tan-quot add-exp-log
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u
3×fma-neg prod-diff
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod difference-of-squares unswap-sqr
1×log1p-udef sub-neg flip3-- diff-log log1p-expm1 flip--
Counts
4 → 97
Calls
4 calls:
5.0ms
(- 1 (* (tan x) (tan x)))
0.0ms
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
17.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series405.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- 1 (* (tan x) (tan x)))
261.0ms
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
51.0ms
(* (tan x) (tan x))
33.0ms
(* (tan x) (tan x))

simplify2.3s

Counts
109 → 109
Iterations
IterNodes
done5000
31732
2784
1277
0115

prune585.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (exp (log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))))
0.3b
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
18×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube tan-quot add-exp-log
6×swap-sqr associate-*r* associate-*l*
5×expm1-log1p-u
4×log-pow insert-posit16 log1p-expm1-u add-log-exp
3×log-prod exp-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×log1p-udef rem-log-exp log1p-expm1
Counts
4 → 92
Calls
4 calls:
5.0ms
(log (exp (log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))))
1.0ms
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
29.0ms
(* (tan x) (tan x))
33.0ms
(* (tan x) (tan x))

series528.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(log (exp (log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))))
207.0ms
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
56.0ms
(* (tan x) (tan x))
58.0ms
(* (tan x) (tan x))

simplify3.2s

Counts
104 → 104
Iterations
IterNodes
done5000
43894
3989
2437
1212
0103

prune521.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
59×*-un-lft-identity
37×times-frac
33×add-cube-cbrt
22×associate-*r*
16×difference-of-squares
11×add-cbrt-cube add-exp-log
9×prod-diff
8×distribute-lft-out--
6×pow1 associate-/l* add-log-exp
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg
2×frac-times cbrt-undiv flip3-+ flip3-- div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv flip-- unswap-sqr associate-/l/
1×clear-num sub-neg frac-2neg diff-log div-sub pow-prod-down associate-*r/ *-commutative fma-udef distribute-lft-out
Counts
4 → 135
Calls
4 calls:
0.0ms
(fma (tan x) (tan x) 1)
15.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
8.0ms
(- 1 (tan x))
35.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(fma (tan x) (tan x) 1)
113.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
36.0ms
(- 1 (tan x))
201.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

simplify1.8s

Counts
147 → 147
Iterations
IterNodes
done5000
21639
1517
0205

prune750.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes263.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done14
114
011

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.1s1443×body1280valid
1.6s1183×body640valid
895.0ms4414×body80valid
507.0ms647×body320valid
126.0ms313×body160valid