Details

Time bar (total: 15.4s)

sample123.0ms

Algorithm
intervals
Results
45.0ms57×body1280valid
26.0ms53×body640valid
23.0ms200×body80valid
8.0ms21×body320valid
4.0ms15×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: 32.0b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (pow t 3.0) (sin k))
3.8b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
5.3b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
27.0b
(* (/ (/ 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:
6.0ms
(* (pow t 3.0) (sin k))
9.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
5.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
18.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
170.0ms
(* (pow t 3.0) (sin k))
317.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
71.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
867.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify54.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010192396
150011978

prune698.0ms

Filtered
196 candidates to 138 candidates (70.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New18610196
Fresh011
Picked101
Done000
Total18711198

Merged error: 25.6b

Counts
198 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (pow t 3.0) (sin k))
3.3b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
6.3b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
19.0b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite51.0ms

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:
9.0ms
(* (pow t 3.0) (sin k))
10.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
8.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
16.0ms
(* (/ (* (/ 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:
174.0ms
(* (pow t 3.0) (sin k))
459.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
353.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
884.0ms
(* (/ (* (/ 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 (25.0ms)

IterNodesCost
09131905
148941506
250011506

prune560.0ms

Filtered
162 candidates to 103 candidates (63.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1539162
Fresh4610
Picked101
Done000
Total15815173

Merged error: 25.1b

Counts
173 → 15

localize28.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.3b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
6.3b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
19.0b
(* (/ (* (/ 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))))

rewrite72.0ms

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)))
15.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
18.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
21.0ms
(* (/ (* (/ 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))))

series2.2s

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
719.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
406.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
956.0ms
(* (/ (* (/ 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))))

simplify61.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011653923
150013194

prune668.0ms

Filtered
220 candidates to 108 candidates (49.1%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New2155220
Fresh01414
Picked101
Done000
Total21619235

Merged error: 24.1b

Counts
235 → 19

localize28.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.3b
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
3.3b
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
19.0b
(* (/ (* (/ 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))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
1780×add-exp-log
960×prod-exp
718×div-exp
196×pow-exp add-cbrt-cube
124×pow-to-exp
96×rec-exp 1-exp
84×cbrt-unprod
70×cbrt-undiv
40×times-frac
37×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
27×associate-*l*
14×associate-*r*
11×pow1
7×associate-*l/
6×associate-/r*
5×div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×frac-times unpow-prod-down associate-*r/ associate-/l/ sqr-pow
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative unswap-sqr
Counts
4 → 478
Calls
4 calls:
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
17.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
21.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
35.0ms
(* (/ (* (/ 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))))

series1.9s

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
396.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
512.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
947.0ms
(* (/ (* (/ 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
490 → 490
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
019609108
150017782

prune715.0ms

Filtered
490 candidates to 123 candidates (25.1%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New4828490
Fresh41418
Picked101
Done000
Total48722509

Merged error: 18.3b

Counts
509 → 22

regimes596.0ms

Accuracy

5.7% (2.5b remaining)

Error of 22.1b against oracle of 19.6b and baseline of 22.3b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06082
16082

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.5s2064×body1280valid
886.0ms1718×body640valid
682.0ms5854×body80valid
328.0ms889×body320valid
111.0ms439×body160valid