Details

Time bar (total: 3.7s)

sample61.0ms

Algorithm
intervals
Results
28.0ms62×body2560valid
12.0ms35×body1280valid
6.0ms42×body640valid
3.0ms74×body80valid
3.0ms25×body320valid
1.0ms18×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

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: 32.4b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b
(- 1.0 (cos x))
17.3b
(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-log-exp
3×fma-neg distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 58
Calls
2 calls:
4.0ms
(- 1.0 (cos x))
8.0ms
(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(- 1.0 (cos x))
42.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify33.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune123.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New541064
Fresh000
Picked101
Done000
Total551065

Merged error: 0.1b

Counts
65 → 10

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 1/24 (pow x 2))
11.3b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×associate-*r*
7×add-exp-log
5×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 39
Calls
2 calls:
5.0ms
(* 1/24 (pow x 2))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series69.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(* 1/24 (pow x 2))
45.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify103.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0139194
1532171
22601171
35001170

prune92.0ms

Filtered
45 candidates to 30 candidates (66.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New45045
Fresh099
Picked011
Done000
Total451055

Merged error: 0.1b

Counts
55 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
54×*-un-lft-identity
46×times-frac
36×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp prod-diff
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×expm1-log1p-u fma-neg associate-/r* log1p-expm1-u div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 132
Calls
3 calls:
17.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series106.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
47.0ms
(/ (- 1.0 (cos x)) x)
18.0ms
(- 1.0 (cos x))

simplify72.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0582999
12640823
25001787

prune210.0ms

Filtered
141 candidates to 91 candidates (64.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1374141
Fresh358
Picked011
Done011
Total14011151

Merged error: 0.1b

Counts
151 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
0.3b
(pow (cos x) 3)
0.4b
(fma (cos x) (cos x) (* 1.0 (cos x)))
1.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
156×add-sqr-sqrt
144×prod-diff
114×unpow-prod-down *-un-lft-identity cube-prod
84×add-cube-cbrt
50×sqr-pow
48×difference-of-squares
26×cube-mult unpow3
25×times-frac associate-/l*
15×distribute-lft-out--
12×fma-neg
10×add-exp-log add-cbrt-cube
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×difference-cubes pow-unpow
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub pow-exp prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv rem-cube-cbrt
Counts
4 → 297
Calls
4 calls:
25.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
2.0ms
(pow (cos x) 3)
1.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
16.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series316.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
28.0ms
(pow (cos x) 3)
49.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
50.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify134.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
07663804
129492790
250012733

prune342.0ms

Filtered
309 candidates to 100 candidates (32.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New3072309
Fresh178
Picked101
Done022
Total30911320

Merged error: 0.0b

Counts
320 → 11

regimes91.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.5b

bsearch77.0ms

Steps
ItersRangePoint
9
0.006602375602419948
2408.9151023461654
0.030982935793368763
10
-7888799.454350161
-0.0014566459989916651
-0.03319237955952178

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04326
14326

end0.0ms

sample1.7s

Algorithm
intervals
Results
781.0ms1630×body2560valid
306.0ms1245×body1280valid
243.0ms1484×body640valid
104.0ms921×body320valid
80.0ms2223×body80valid
44.0ms497×body160valid