Details

Time bar (total: 6.7s)

sample154.0ms

Algorithm
intervals
Results
84.0ms60×body2560valid
42.0ms97×body1280valid
12.0ms50×body640valid
4.0ms24×body320valid
1.0ms14×body160valid
1.0ms11×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune3.0ms

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: 32.4b

Counts
2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:
6.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series53.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify79.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune199.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New461258
Fresh000
Picked101
Done000
Total471259

Merged error: 0.1b

Counts
59 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/240 (pow x 5)) (* 1/2 x))
0.0b
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b
(* 1/24 (pow x 3))
0.2b
(* 1/240 (pow x 5))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sum-log sqr-pow
2×+-commutative pow-to-exp flip3-+ pow-exp *-commutative cbrt-unprod flip-+
1×cube-mult associate-+r+ unpow3
Counts
4 → 80
Calls
4 calls:
4.0ms
(+ (* 1/240 (pow x 5)) (* 1/2 x))
7.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
8.0ms
(* 1/24 (pow x 3))
5.0ms
(* 1/240 (pow x 5))

series268.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(+ (* 1/240 (pow x 5)) (* 1/2 x))
55.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
38.0ms
(* 1/24 (pow x 3))
47.0ms
(* 1/240 (pow x 5))

simplify53.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0355458
11538429
25002428

prune246.0ms

Filtered
92 candidates to 59 candidates (64.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New91192
Fresh01111
Picked101
Done000
Total9212104

Merged error: 0.1b

Counts
104 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5))) (* 1/2 x))
0.0b
(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
0.1b
(* 1/24 (pow x 3))
0.2b
(* 1/240 (pow x 5))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sum-log sqr-pow
2×+-commutative pow-to-exp flip3-+ pow-exp *-commutative cbrt-unprod flip-+
1×cube-mult associate-+l+ unpow3
Counts
4 → 80
Calls
4 calls:
7.0ms
(+ (+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5))) (* 1/2 x))
4.0ms
(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
6.0ms
(* 1/24 (pow x 3))
5.0ms
(* 1/240 (pow x 5))

series280.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(+ (+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5))) (* 1/2 x))
137.0ms
(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
36.0ms
(* 1/24 (pow x 3))
52.0ms
(* 1/240 (pow x 5))

simplify58.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0349479
11531448
25001447

prune244.0ms

Filtered
92 candidates to 59 candidates (64.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh01111
Picked011
Done000
Total9212104

Merged error: 0.1b

Counts
104 → 12

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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:
8.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms
(/ (sin x) (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))

series89.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
38.0ms
(/ (sin x) (- 1.0 (cos x)))
18.0ms
(- 1.0 (cos x))

simplify61.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05101593
123961450
250021337

prune272.0ms

Filtered
168 candidates to 85 candidates (50.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1671168
Fresh01010
Picked101
Done011
Total16812180

Merged error: 0.1b

Counts
180 → 12

regimes191.0ms

Accuracy

98.4% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 31.8b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04434
14434

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.2s1657×body2560valid
1.2s2733×body1280valid
432.0ms1881×body640valid
148.0ms928×body320valid
47.0ms431×body160valid
24.0ms369×body80valid
5.0ms1×body5120valid

Profiling

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