Details

Time bar (total: 20.7s)

sample289.0ms

Algorithm
intervals
Results
61.0ms57×body1280valid
42.0ms49×body640valid
24.0ms130×body80valid
8.0ms14×body320valid
2.0ms6×body160valid

simplify106.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

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

rewrite82.0ms

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
33.0ms
(* (tan x) (tan x))
20.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
19.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (* (tan x) (tan x)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
66.0ms
(* (tan x) (tan x))
39.0ms
(- 1 (* (tan x) (tan x)))
35.0ms
(* (tan x) (tan x))

simplify1.4s

Counts
140 → 140

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
27×prod-diff
13×pow1
11×distribute-rgt-in distribute-lft-in
9×associate-*r*
8×add-cbrt-cube add-exp-log add-log-exp
7×associate-*l*
5×frac-times
4×expm1-log1p-u flip3-+ flip3-- tan-quot flip-+ insert-posit16 log1p-expm1-u flip-- difference-of-squares
3×sub-neg fma-def fma-neg swap-sqr associate-*l/ associate-*r/
2×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 → 134
Calls
4 calls:
Slowest
30.0ms
(* (tan x) (tan x))
26.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
5.0ms
(- 1 (tan x))
5.0ms
(+ 1 (tan x))

series196.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
58.0ms
(* (tan x) (tan x))
29.0ms
(- 1 (tan x))
26.0ms
(+ 1 (tan x))

simplify1.1s

Counts
146 → 146

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
62×*-un-lft-identity
37×times-frac
34×add-cube-cbrt
22×associate-*r*
16×difference-of-squares
11×add-cbrt-cube add-exp-log
9×prod-diff
8×distribute-lft-out-- add-log-exp
6×pow1 associate-/l*
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×associate-/r* fma-def flip3-+ fma-neg flip-+
2×frac-times cbrt-undiv flip3-- div-exp associate-*l/ prod-exp cbrt-unprod div-inv flip-- distribute-lft-out unswap-sqr associate-/l/
1×+-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub pow-prod-down associate-*r/ *-commutative
Counts
4 → 142
Calls
4 calls:
Slowest
52.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
14.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
9.0ms
(+ 1 (tan x))
5.0ms
(- 1 (tan x))

series317.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
95.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
32.0ms
(- 1 (tan x))
23.0ms
(+ 1 (tan x))

simplify2.7s

Counts
154 → 154

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
85×*-un-lft-identity
61×times-frac
56×log-pow add-cube-cbrt
54×exp-prod
34×associate-*r*
22×exp-sum
18×prod-diff difference-of-squares
14×pow1 log-prod
11×add-cbrt-cube add-exp-log
10×associate-/l*
9×distribute-lft-out--
7×add-log-exp
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×associate-/r* exp-diff
2×frac-times cbrt-undiv log-div sub-neg flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr rem-exp-log
1×clear-num frac-2neg diff-log div-sub rem-log-exp pow-prod-down associate-*r/ *-commutative distribute-lft-out
Counts
4 → 183
Calls
4 calls:
Slowest
59.0ms
(/ (log (exp (- 1 (tan x)))) (fma (tan x) (tan x) 1))
53.0ms
(* (+ 1 (tan x)) (/ (log (exp (- 1 (tan x)))) (fma (tan x) (tan x) 1)))
24.0ms
(log (exp (- 1 (tan x))))
12.0ms
(exp (- 1 (tan x)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(* (+ 1 (tan x)) (/ (log (exp (- 1 (tan x)))) (fma (tan x) (tan x) 1)))
78.0ms
(/ (log (exp (- 1 (tan x)))) (fma (tan x) (tan x) 1))
55.0ms
(exp (- 1 (tan x)))
40.0ms
(log (exp (- 1 (tan x))))

simplify1.0s

Counts
195 → 195

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes427.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.6s1458×body1280valid
1.7s1302×body640valid
973.0ms4316×body80valid
482.0ms642×body320valid
158.0ms282×body160valid