Details

Time bar (total: 11.2s)

sample303.0ms

Algorithm
intervals
Results
148.0ms55×body2560valid
80.0ms90×body1280valid
32.0ms66×body640valid
11.0ms12×body160valid
9.0ms26×body320valid
2.0ms7×body80valid

simplify22.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
02297
12297

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.6b

Counts
2 → 1

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.0b
(- 1.0 (cos x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
13.0ms
(/ (- 1.0 (cos x)) (sin x))
7.0ms
(- 1.0 (cos x))

series22.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(/ (- 1.0 (cos x)) (sin x))
6.0ms
(- 1.0 (cos x))

simplify79.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
05058608

prune230.0ms

Filtered
42 candidates to 58 candidates (-38.1%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New421658
Fresh000
Picked101
Done000
Total431659

Merged error: 0.2b

Counts
59 → 16

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b
(/ (sin x) (- 1.0 (cos x)))
2.0b
(- 1.0 (cos x))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
105×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
17×distribute-lft-out-- difference-of-squares
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- flip-- div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp frac-2neg 1-exp clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 159
Calls
3 calls:
18.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
13.0ms
(/ (sin x) (- 1.0 (cos x)))
7.0ms
(- 1.0 (cos x))

series38.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
16.0ms
(/ (sin x) (- 1.0 (cos x)))
6.0ms
(- 1.0 (cos x))

simplify121.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
050932255

prune425.0ms

Filtered
99 candidates to 168 candidates (-69.7%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1617168
Fresh51015
Picked101
Done000
Total16717184

Merged error: 0.2b

Counts
184 → 17

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (sin x))
0.2b
(* (- 1.0 (cos x)) (/ 1 (sin x)))
2.0b
(- 1.0 (cos x))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×*-un-lft-identity
20×times-frac
19×add-cube-cbrt
16×add-exp-log
13×associate-*r*
10×add-cbrt-cube
6×pow1
5×associate-*l* add-log-exp
4×div-exp prod-exp
3×flip3-- associate-/r* flip-- associate-/l* unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv distribute-lft-out-- difference-of-squares
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
3 → 87
Calls
3 calls:
7.0ms
(/ 1 (sin x))
18.0ms
(* (- 1.0 (cos x)) (/ 1 (sin x)))
7.0ms
(- 1.0 (cos x))

series28.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(/ 1 (sin x))
14.0ms
(* (- 1.0 (cos x)) (/ 1 (sin x)))
6.0ms
(- 1.0 (cos x))

simplify84.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
05161781

prune253.0ms

Filtered
56 candidates to 96 candidates (-71.4%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New94296
Fresh21416
Picked101
Done000
Total9716113

Merged error: 0.2b

Counts
113 → 16

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x))
0.4b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
1.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
21×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
9×add-cube-cbrt sqr-pow
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
3×pow-unpow associate-*r* associate-*l*
2×flip3-+ associate-*l/ flip-+
1×difference-cubes +-commutative cube-mult pow-to-exp sub-neg flip3-- pow-pow diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 89
Calls
4 calls:
13.0ms
(* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x))
5.0ms
(pow (cos x) 3)
8.0ms
(+ 1.0 (cos x))
27.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series50.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x)))) (sin x))
9.0ms
(pow (cos x) 3)
4.0ms
(+ 1.0 (cos x))
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify55.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
057571110

prune288.0ms

Filtered
61 candidates to 101 candidates (-65.6%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New983101
Fresh11415
Picked101
Done000
Total10017117

Merged error: 0.1b

Counts
117 → 17

regimes392.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.9b

bsearch88.0ms

Steps
ItersRangePoint
10
0.01683730658649282
12785707414306.22
0.019474268356794753
10
-0.2101619750885166
-2.51237587459879e-12
-0.018586529511459986

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
08274
18274

end0.0ms

sample8.4s

Algorithm
intervals
Results
4.2s1663×body2560valid
2.4s2741×body1280valid
858.0ms1822×body640valid
308.0ms938×body320valid
106.0ms475×body160valid
48.0ms357×body80valid
34.0ms4×body5120valid

Profiling

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