Details

Time bar (total: 4.7s)

sample117.0ms

Algorithm
intervals
Results
54.0ms116×body1280valid
24.0ms25×body2560valid
14.0ms50×body640valid
4.0ms21×body320valid
2.0ms34×body80valid
2.0ms10×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0107
1107

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.8b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (sin (+ x eps)) (sin x))
3.8b
(sin (+ x eps))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt sin-sum add-cbrt-cube
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
6.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series13.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(- (sin (+ x eps)) (sin x))
5.0ms
(sin (+ x eps))

simplify53.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
05212271

prune53.0ms

Filtered
23 candidates to 30 candidates (-30.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New25530
Fresh000
Picked101
Done000
Total26531

Merged error: 0.3b

Counts
31 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
0.0b
(+ x (+ x eps))
0.3b
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.7b
(cos (/ (+ x (+ x eps)) 2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×associate-*l*
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×sum-log distribute-lft-out
2×*-commutative sin-cos-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 60
Calls
4 calls:
7.0ms
(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
5.0ms
(+ x (+ x eps))
7.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms
(cos (/ (+ x (+ x eps)) 2))

series33.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
4.0ms
(+ x (+ x eps))
10.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify44.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
05004886

prune146.0ms

Filtered
53 candidates to 72 candidates (-35.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New65772
Fresh134
Picked011
Done000
Total661177

Merged error: 0.3b

Counts
77 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
0.5b
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
0.6b
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
3.7b
(cos (/ (+ x (+ x eps)) 2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
24×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity associate-*r*
10×unpow-prod-down cube-prod
7×pow1 add-exp-log
6×add-cbrt-cube
5×unswap-sqr
4×add-log-exp sqr-pow
3×cube-mult pow-unpow unpow3 associate-*l*
1×pow-to-exp pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 85
Calls
4 calls:
8.0ms
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
2.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
2.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series34.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
12.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
5.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
5.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify40.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
053581255

prune163.0ms

Filtered
55 candidates to 97 candidates (-76.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New95297
Fresh279
Picked101
Done011
Total9810108

Merged error: 0.2b

Counts
108 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ x (+ x eps)) 2)))
0.3b
(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.5b
(log (exp (cos (/ (+ x (+ x eps)) 2))))
3.7b
(cos (/ (+ x (+ x eps)) 2))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-exp-log add-cbrt-cube
5×add-log-exp
3×distribute-rgt-in distribute-lft-in associate-*l*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 61
Calls
4 calls:
7.0ms
(exp (cos (/ (+ x (+ x eps)) 2)))
15.0ms
(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
7.0ms
(log (exp (cos (/ (+ x (+ x eps)) 2))))
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series31.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(exp (cos (/ (+ x (+ x eps)) 2)))
11.0ms
(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
5.0ms
(log (exp (cos (/ (+ x (+ x eps)) 2))))
5.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify69.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
04934934
14934934

prune124.0ms

Filtered
54 candidates to 73 candidates (-35.2%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New73073
Fresh088
Picked011
Done011
Total731083

Merged error: 0.2b

Counts
83 → 10

regimes183.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 14.8b

bsearch79.0ms

Steps
ItersRangePoint
11
6.401380870969369e-19
14704714838.838829
6.924959549953746e-09
6
-483.0583385386567
-60.40944958396893
-61.159237417823334

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03551
13551

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.6s3223×body1280valid
710.0ms707×body2560valid
549.0ms1851×body640valid
160.0ms786×body320valid
83.0ms1103×body80valid
45.0ms330×body160valid

Profiling

Loading profile data...