Details

Time bar (total: 14.2s)

sample124.0ms

Algorithm
intervals
Results
47.0ms69×body1280valid
28.0ms60×body640valid
20.0ms193×body80valid
9.0ms29×body320valid
2.0ms9×body160valid

simplify32.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
04813
116113
294413
3500212

prune15.0ms

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: 29.5b

Counts
2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow t 3.0) (sin k))
3.9b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
6.5b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
22.0b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite44.0ms

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:
5.0ms
(* (pow t 3.0) (sin k))
9.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
4.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
17.0ms
(* (/ (/ 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:
171.0ms
(* (pow t 3.0) (sin k))
322.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
73.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
844.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010192396
150011978

prune759.0ms

Filtered
196 candidates to 138 candidates (70.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1879196
Fresh011
Picked101
Done000
Total18810198

Merged error: 23.1b

Counts
198 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.4b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
3.4b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
17.5b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
114×add-exp-log
74×add-cbrt-cube
46×prod-exp
42×div-exp
33×add-sqr-sqrt
28×times-frac
26×cbrt-undiv add-cube-cbrt *-un-lft-identity cbrt-unprod
16×associate-*r*
15×associate-*l*
8×pow1
6×associate-/r*
5×div-inv
4×expm1-log1p-u pow-to-exp pow-exp 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 → 152
Calls
4 calls:
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
8.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
10.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
16.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
342.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
449.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
854.0ms
(* (/ (* (/ 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
164 → 164
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08691986
148481580
250011580

prune619.0ms

Filtered
164 candidates to 106 candidates (64.6%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1568164
Fresh549
Picked101
Done000
Total16212174

Merged error: 22.6b

Counts
174 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.4b
(/ (* 2.0 (/ (/ l (sin k)) (pow t 3.0))) (tan k))
5.4b
(/ (/ l (sin k)) (pow t 3.0))
17.5b
(* (/ (* 2.0 (/ (/ l (sin k)) (pow t 3.0))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
188×times-frac
138×add-exp-log
112×add-sqr-sqrt
107×add-cube-cbrt *-un-lft-identity
70×div-exp add-cbrt-cube
42×unpow-prod-down
39×prod-exp
30×cbrt-undiv
19×cbrt-unprod
17×associate-/l*
14×sqr-pow
13×associate-*r* associate-/r* div-inv
8×pow-to-exp associate-*l* pow-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×tan-quot associate-*r/ associate-/r/ associate-/l/ unswap-sqr
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 259
Calls
4 calls:
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
19.0ms
(/ (* 2.0 (/ (/ l (sin k)) (pow t 3.0))) (tan k))
9.0ms
(/ (/ l (sin k)) (pow t 3.0))
21.0ms
(* (/ (* 2.0 (/ (/ l (sin k)) (pow t 3.0))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series999.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
318.0ms
(/ (* 2.0 (/ (/ l (sin k)) (pow t 3.0))) (tan k))
211.0ms
(/ (/ l (sin k)) (pow t 3.0))
389.0ms
(* (/ (* 2.0 (/ (/ l (sin k)) (pow t 3.0))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify66.0ms

Algorithm
egg-herbie
Counts
271 → 271
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012133156
150022767

prune1.1s

Filtered
271 candidates to 186 candidates (68.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New26110271
Fresh6511
Picked101
Done000
Total26815283

Merged error: 13.8b

Counts
283 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.4b
(/ (* 2.0 (* (/ l (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (/ 1 (sin k)) (pow (cbrt t) 3.0)))) (tan k))
6.6b
(/ l (pow (* (cbrt t) (cbrt t)) 3.0))
17.5b
(* (/ (* 2.0 (* (/ l (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (/ 1 (sin k)) (pow (cbrt t) 3.0)))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
1336×add-exp-log
700×div-exp
569×prod-exp
151×add-cbrt-cube
140×pow-exp
100×pow-to-exp
62×cbrt-undiv
57×cbrt-unprod
45×rec-exp 1-exp
40×times-frac
38×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
13×associate-*r*
11×associate-/r*
8×associate-*l*
7×associate-/l*
6×pow1
5×associate-*r/ div-inv
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp sqr-pow
3×frac-2neg clear-num associate-/l/
2×tan-quot frac-times associate-*l/ associate-/r/ unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 358
Calls
4 calls:
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
32.0ms
(/ (* 2.0 (* (/ l (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (/ 1 (sin k)) (pow (cbrt t) 3.0)))) (tan k))
5.0ms
(/ l (pow (* (cbrt t) (cbrt t)) 3.0))
38.0ms
(* (/ (* 2.0 (* (/ l (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (/ 1 (sin k)) (pow (cbrt t) 3.0)))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
666.0ms
(/ (* 2.0 (* (/ l (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (/ 1 (sin k)) (pow (cbrt t) 3.0)))) (tan k))
184.0ms
(/ l (pow (* (cbrt t) (cbrt t)) 3.0))
607.0ms
(* (/ (* 2.0 (* (/ l (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (/ 1 (sin k)) (pow (cbrt t) 3.0)))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify86.0ms

Algorithm
egg-herbie
Counts
370 → 370
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
017056902
150015924

prune743.0ms

Filtered
370 candidates to 121 candidates (32.7%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New3628370
Fresh31114
Picked101
Done000
Total36619385

Merged error: 12.9b

Counts
385 → 19

regimes513.0ms

Accuracy

59.1% (3.9b remaining)

Error of 17.2b against oracle of 13.4b and baseline of 22.8b

bsearch326.0ms

Steps
ItersRangePoint
10
1.275832223595475e-96
1.437759422872514e-82
1.0019272506601638e-82
9
-1.0298940069853194e-81
-5.48784537257136e-90
-1.938413813152478e-87

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07059
17259
27259

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.4s2070×body1280valid
809.0ms1700×body640valid
622.0ms5961×body80valid
282.0ms832×body320valid
92.0ms410×body160valid