Details

Time bar (total: 7.9s)

sample142.0ms

Algorithm
intervals
Results
66.0ms48×body2560valid
46.0ms93×body1280valid
15.0ms64×body640valid
5.0ms29×body320valid
2.0ms16×body160valid
0.0ms6×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.1b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.2b
(- 1.0 (cos x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series60.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(/ (- 1.0 (cos x)) (sin x))
18.0ms
(- 1.0 (cos x))

simplify36.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0292569
1965460
25002460

prune181.0ms

Filtered
74 candidates to 51 candidates (68.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New591574
Fresh000
Picked101
Done000
Total601575

Merged error: 0.3b

Counts
75 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b
(log (- 1.0 (cos x)))
0.2b
(exp (log (- 1.0 (cos x))))
1.2b
(- 1.0 (cos x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt *-un-lft-identity
31×add-cube-cbrt
30×log-prod
25×exp-sum
24×times-frac
9×prod-diff
8×associate-/l*
7×distribute-lft-out-- difference-of-squares
6×pow1 add-exp-log log-div add-cbrt-cube add-log-exp
4×expm1-log1p-u exp-prod flip3-- exp-diff flip-- log1p-expm1-u
3×fma-neg associate-/r*
2×log-pow associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num div-inv rem-exp-log
Counts
4 → 118
Calls
4 calls:
8.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
4.0ms
(log (- 1.0 (cos x)))
4.0ms
(exp (log (- 1.0 (cos x))))
4.0ms
(- 1.0 (cos x))

series153.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
76.0ms
(log (- 1.0 (cos x)))
18.0ms
(exp (log (- 1.0 (cos x))))
19.0ms
(- 1.0 (cos x))

simplify41.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03541019
11045861
25001817

prune266.0ms

Filtered
130 candidates to 80 candidates (61.5%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1246130
Fresh41014
Picked011
Done000
Total12817145

Merged error: 0.2b

Counts
145 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.7b
(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
0.8b
(log (- (pow 1.0 3) (pow (cos x) 3)))
1.0b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
129×add-sqr-sqrt
101×*-un-lft-identity
99×unpow-prod-down cube-prod
81×add-cube-cbrt
41×sqr-pow
32×difference-of-squares
28×log-prod
25×cube-mult unpow3
12×fma-neg
10×distribute-lft-out--
8×add-log-exp
6×pow1 add-exp-log
4×expm1-log1p-u log-div add-cbrt-cube log1p-expm1-u
2×difference-cubes flip3-- flip3-+ rem-log-exp log-pow flip-- flip-+
1×+-commutative sub-neg sqr-cos associate-+l+ distribute-rgt-out fma-def diff-log sum-log
Counts
4 → 262
Calls
4 calls:
5.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
6.0ms
(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
17.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series350.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
137.0ms
(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
118.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))
49.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify142.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
07323354
128022422
250022404

prune486.0ms

Filtered
274 candidates to 91 candidates (33.2%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New2695274
Fresh11415
Picked101
Done011
Total27120291

Merged error: 0.2b

Counts
291 → 20

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.7b
(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
0.8b
(log (- (pow 1.0 3) (pow (cos x) 3)))
1.0b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
129×add-sqr-sqrt
101×*-un-lft-identity
99×unpow-prod-down cube-prod
81×add-cube-cbrt
41×sqr-pow
32×difference-of-squares
28×log-prod
25×cube-mult unpow3
12×fma-neg
10×distribute-lft-out--
8×add-log-exp
6×pow1 add-exp-log
4×expm1-log1p-u log-div add-cbrt-cube log1p-expm1-u
2×difference-cubes flip3-- flip3-+ rem-log-exp log-pow flip-- flip-+
1×+-commutative sub-neg sqr-cos associate-+l+ distribute-rgt-out fma-def diff-log sum-log
Counts
4 → 262
Calls
4 calls:
6.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
6.0ms
(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
22.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series352.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
142.0ms
(log (+ (* 1.0 1.0) (+ (* (cos x) (cos x)) (* 1.0 (cos x)))))
113.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))
55.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify148.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
07323322
128062390
250012376

prune484.0ms

Filtered
274 candidates to 91 candidates (33.2%)
Pruning

22 alts after pruning (20 fresh and 2 done)

PrunedKeptTotal
New2722274
Fresh01818
Picked011
Done011
Total27222294

Merged error: 0.2b

Counts
294 → 22

regimes435.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.0b

bsearch110.0ms

Steps
ItersRangePoint
11
3.029362037509861e-19
14.716166499582775
0.021329078951286103
11
-2193661101726697.2
-1.4639597033977343e-08
-0.018270236035180427

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04331
14331

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.2s1600×body2560valid
1.3s2777×body1280valid
451.0ms1854×body640valid
149.0ms923×body320valid
59.0ms467×body160valid
32.0ms374×body80valid
26.0ms5×body5120valid