Details

Time bar (total: 16.8s)

sample120.0ms

Algorithm
intervals
Results
51.0ms69×body1280valid
19.0ms42×body640valid
19.0ms188×body80valid
9.0ms29×body320valid
4.0ms17×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.8b

Counts
2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (pow t 3.0) (sin k))
4.2b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
4.2b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
24.3b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
73×times-frac
56×add-sqr-sqrt
50×div-exp
41×add-cube-cbrt *-un-lft-identity
40×prod-exp
33×associate-*l*
30×cbrt-undiv
22×cbrt-unprod
11×div-inv
10×associate-*r*
8×associate-/l*
7×unswap-sqr
6×pow1 associate-/r*
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative sqr-pow
1×frac-times associate-*r/ pow-prod-down associate-*l/ associate-/l/
Counts
4 → 184
Calls
4 calls:
9.0ms
(* (pow t 3.0) (sin k))
5.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
9.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
19.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (pow t 3.0) (sin k))
74.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
337.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
881.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify53.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010192396
150011978

prune773.0ms

Filtered
196 candidates to 138 candidates (70.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1888196
Fresh011
Picked101
Done000
Total1899198

Merged error: 24.5b

Counts
198 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (pow t 3.0) (sin k))
4.0b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
5.5b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
17.6b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
49×prod-exp
41×div-exp
33×add-sqr-sqrt
27×cbrt-unprod
25×cbrt-undiv
22×associate-*l*
21×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
8×pow1
6×unswap-sqr
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-/r* *-commutative
2×tan-quot pow-prod-down associate-/r/ sqr-pow
1×frac-times frac-2neg associate-*r/ clear-num associate-/l/ associate-/l*
Counts
4 → 150
Calls
4 calls:
6.0ms
(* (pow t 3.0) (sin k))
10.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
9.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
20.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (pow t 3.0) (sin k))
469.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
346.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
895.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify121.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09131905
148941506
250011506

prune597.0ms

Filtered
162 candidates to 103 candidates (63.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1566162
Fresh538
Picked101
Done000
Total1629171

Merged error: 24.0b

Counts
171 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
4.0b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
5.5b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
17.6b
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
436×add-exp-log
240×prod-exp
146×div-exp
100×add-cbrt-cube
48×pow-exp
40×cbrt-unprod
34×cbrt-undiv
33×add-sqr-sqrt
32×pow-to-exp
28×times-frac
26×add-cube-cbrt *-un-lft-identity
16×associate-*r*
15×associate-*l*
8×pow1
6×associate-/r*
5×div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*l/ unswap-sqr
2×tan-quot frac-2neg pow-prod-down clear-num associate-/r/ *-commutative
1×frac-times associate-*r/ associate-/l/
Counts
4 → 208
Calls
4 calls:
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
21.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
14.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
22.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.0s

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
528.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
423.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
996.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify58.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011653923
150013194

prune754.0ms

Filtered
220 candidates to 107 candidates (48.6%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2137220
Fresh178
Picked101
Done000
Total21514229

Merged error: 21.5b

Counts
229 → 14

localize231.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)
2.6b
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
4.0b
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
17.6b
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
1794×add-exp-log
968×prod-exp
721×div-exp
203×add-cbrt-cube
197×pow-exp
125×pow-to-exp
96×rec-exp 1-exp
88×cbrt-unprod
71×cbrt-undiv
34×add-sqr-sqrt times-frac associate-*l*
27×add-cube-cbrt *-un-lft-identity
17×associate-*r*
13×pow1
8×associate-*l/
5×pow-prod-down div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times unpow-prod-down associate-*r/ associate-/r* *-commutative associate-/l/ unswap-sqr sqr-pow
2×tan-quot associate-/r/
1×frac-2neg clear-num associate-/l*
Counts
4 → 480
Calls
4 calls:
10.0ms
(* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)
18.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
22.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
32.0ms
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.4s

Counts
4 → 12
Calls
4 calls:
431.0ms
(* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)
412.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
529.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
997.0ms
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify115.0ms

Algorithm
egg-herbie
Counts
492 → 492
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
020449167
150018223

prune885.0ms

Filtered
492 candidates to 131 candidates (26.6%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New4839492
Fresh4913
Picked101
Done000
Total48818506

Merged error: 17.9b

Counts
506 → 18

regimes778.0ms

Accuracy

8.3% (2.6b remaining)

Error of 21.1b against oracle of 18.5b and baseline of 21.3b

bsearch507.0ms

Steps
ItersRangePoint
7
6.66182219120084e+105
6.051047097450507e+107
2.4369144430222617e+106
7
1.3001508934084185e-200
5.480851928629369e-199
2.5281842998290106e-199
6
-1.330720283218611e-187
-8.353072910944365e-189
-3.065023570351247e-188
10
-2.56321445767563e+134
-6.4596291545743535e+122
-4.434550440782941e+123

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
071112
171112

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.4s2035×body1280valid
829.0ms1745×body640valid
634.0ms5959×body80valid
309.0ms903×body320valid
95.0ms404×body160valid