Details

Time bar (total: 7.0s)

analyze500.0ms

Algorithm
search

sample156.0ms

Algorithm
intervals
Results
81.0ms56×body2560valid
43.0ms83×body1280valid
17.0ms67×body640valid
5.0ms29×body320valid
1.0ms13×body80valid
1.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.5b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
1.5b
(- 1.0 (cos x))

rewrite11.0ms

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))

series12.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

simplify79.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune129.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New451358
Fresh000
Picked101
Done000
Total461359

Merged error: 0.1b

Counts
59 → 13

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))
0.3b
(* 1/240 (pow x 5))

rewrite25.0ms

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))
8.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
6.0ms
(* 1/24 (pow x 3))
5.0ms
(* 1/240 (pow x 5))

series26.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (* 1/240 (pow x 5)) (* 1/2 x))
6.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms
(* 1/24 (pow x 3))
5.0ms
(* 1/240 (pow x 5))

simplify55.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0355471
11532436
25002435

prune165.0ms

Filtered
59 candidates to 92 candidates (-55.9%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh01212
Picked011
Done000
Total9213105

Merged error: 0.1b

Counts
105 → 13

localize9.0ms

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)))
1.5b
(- 1.0 (cos x))

rewrite29.0ms

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:
11.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms
(/ (sin x) (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series19.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
8.0ms
(/ (sin x) (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))

simplify61.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05101593
123961450
250021337

prune151.0ms

Filtered
84 candidates to 168 candidates (-100.0%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1653168
Fresh2911
Picked101
Done011
Total16813181

Merged error: 0.1b

Counts
181 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (- 1.0 (cos x)))
0.1b
(/ (log (exp (- 1.0 (cos x)))) (sin x))
1.5b
(- 1.0 (cos x))
1.6b
(log (exp (- 1.0 (cos x))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt *-un-lft-identity
30×exp-prod log-pow
27×times-frac
25×add-cube-cbrt
9×pow1 associate-/l* add-log-exp
7×distribute-lft-out-- difference-of-squares
6×add-exp-log add-cbrt-cube
5×log-prod
4×exp-sum
3×sub-neg exp-diff associate-/r*
2×log-div diff-log rem-exp-log
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp rem-log-exp clear-num flip-- div-inv
Counts
4 → 103
Calls
4 calls:
4.0ms
(exp (- 1.0 (cos x)))
8.0ms
(/ (log (exp (- 1.0 (cos x)))) (sin x))
3.0ms
(- 1.0 (cos x))
5.0ms
(log (exp (- 1.0 (cos x))))

series23.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(exp (- 1.0 (cos x)))
8.0ms
(/ (log (exp (- 1.0 (cos x)))) (sin x))
3.0ms
(- 1.0 (cos x))
3.0ms
(log (exp (- 1.0 (cos x))))

simplify105.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0295766
1890686
23427674
35001672

prune116.0ms

Filtered
73 candidates to 115 candidates (-57.5%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1114115
Fresh3811
Picked011
Done011
Total11414128

Merged error: 0.1b

Counts
128 → 14

regimes210.0ms

Accuracy

97.3% (0.9b remaining)

Error of 1.1b against oracle of 0.2b and baseline of 32.5b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03632
13632

end0.0ms

analyze496.0ms

Algorithm
search

sample4.6s

Algorithm
intervals
Results
2.3s1625×body2560valid
1.4s2762×body1280valid
489.0ms1906×body640valid
155.0ms907×body320valid
55.0ms460×body160valid
24.0ms336×body80valid
14.0ms4×body5120valid

Profiling

Loading profile data...