Details

Time bar (total: 19.2s)

sample177.0ms

Algorithm
intervals
Results
27.0ms46×body1280valid
18.0ms49×body640valid
9.0ms125×body80valid
6.0ms21×body320valid
3.0ms15×body160valid

simplify485.0ms

Counts
1 → 1
Iterations
IterNodes
done45
645
543
437
329
222
113
07

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(- 1.0 (* (tan x) (tan x)))
0.2b
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
18×pow1
12×times-frac
10×add-cbrt-cube add-exp-log
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×expm1-log1p-u log1p-expm1-u associate-/l*
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 → 119
Calls
4 calls:
8.0ms
(- 1.0 (* (tan x) (tan x)))
40.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
13.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series277.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- 1.0 (* (tan x) (tan x)))
126.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
44.0ms
(* (tan x) (tan x))
47.0ms
(* (tan x) (tan x))

simplify1.8s

Counts
131 → 131
Iterations
IterNodes
done5001
21697
1376
0151

prune793.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b
(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×pow1
12×times-frac
10×add-cbrt-cube add-exp-log
8×tan-quot
6×swap-sqr associate-*r* associate-*l*
5×expm1-log1p-u
4×log1p-expm1-u associate-/l* add-log-exp difference-of-squares
3×associate-/r*
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr associate-/l/
1×cbrt-undiv log1p-udef clear-num frac-2neg flip3-+ flip3-- div-sub div-exp log1p-expm1 flip-+ div-inv flip--
Counts
4 → 109
Calls
4 calls:
36.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
1.0ms
(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
23.0ms
(* (tan x) (tan x))
24.0ms
(* (tan x) (tan x))

series634.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
369.0ms
(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
63.0ms
(* (tan x) (tan x))
65.0ms
(* (tan x) (tan x))

simplify1.6s

Counts
121 → 121
Iterations
IterNodes
done5001
21803
1411
0162

prune752.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.2b
(* (sin x) (tan x))
0.2b
(log1p (/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
28×*-un-lft-identity
20×add-cube-cbrt
15×times-frac
13×pow1
10×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
5×expm1-log1p-u tan-quot associate-/l*
4×log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×associate-/r* swap-sqr
2×pow-prod-down prod-exp associate-*r/ associate-/r/ *-commutative cbrt-unprod unswap-sqr associate-/l/
1×pow2 frac-times cbrt-undiv log1p-udef clear-num frac-2neg flip3-+ pow-plus flip3-- div-sub div-exp associate-*l/ log1p-expm1 pow-sqr pow-prod-up flip-+ div-inv flip--
Counts
4 → 104
Calls
4 calls:
50.0ms
(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
19.0ms
(* (sin x) (tan x))
1.0ms
(log1p (/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x)))))
22.0ms
(* (tan x) (tan x))

series593.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
61.0ms
(* (sin x) (tan x))
360.0ms
(log1p (/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x)))))
38.0ms
(* (tan x) (tan x))

simplify1.7s

Counts
116 → 116
Iterations
IterNodes
done5002
22272
1495
0195

prune851.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
0.2b
(* (sin x) (tan x))
0.2b
(log1p (/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))))
0.3b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
55×times-frac
52×*-un-lft-identity
44×add-cube-cbrt
20×add-cbrt-cube add-exp-log
16×associate-*r* associate-*l*
13×pow1 swap-sqr
5×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l* unswap-sqr
4×log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×associate-/r*
2×pow-prod-down associate-*r/ associate-/r/ *-commutative associate-/l/
1×pow2 frac-times log1p-udef clear-num frac-2neg flip3-+ pow-plus flip3-- div-sub associate-*l/ tan-quot log1p-expm1 pow-sqr pow-prod-up flip-+ flip--
Counts
4 → 143
Calls
4 calls:
46.0ms
(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
19.0ms
(* (sin x) (tan x))
1.0ms
(log1p (/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))))
53.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
60.0ms
(* (sin x) (tan x))
426.0ms
(log1p (/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))))
84.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify2.7s

Counts
155 → 155
Iterations
IterNodes
done5000
24696
1796
0270

prune998.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes338.0ms

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
done9
19
08

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s1532×body1280valid
1.3s1251×body640valid
617.0ms4281×body80valid
231.0ms603×body320valid
98.0ms333×body160valid