Details

Time bar (total: 16.4s)

sample129.0ms

Algorithm
intervals
Results
44.0ms54×body1280valid
27.0ms52×body640valid
21.0ms192×body80valid
12.0ms32×body320valid
3.0ms13×body160valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
04813
116113
294413
3500212

prune13.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize27.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
3.9b
(* (pow t 3.0) (sin k))
5.9b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
26.1b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite56.0ms

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:
8.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
6.0ms
(* (pow t 3.0) (sin k))
4.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
30.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
327.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
170.0ms
(* (pow t 3.0) (sin k))
72.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
1.1s
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010192396
150011978

prune733.0ms

Filtered
196 candidates to 138 candidates (70.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.3b

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
3.9b
(* (pow t 3.0) (sin k))
5.9b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
19.1b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite83.0ms

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:
11.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
6.0ms
(* (pow t 3.0) (sin k))
13.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
46.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.8s

Counts
4 → 12
Calls
4 calls:
454.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
166.0ms
(* (pow t 3.0) (sin k))
330.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
866.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify114.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09131905
148941506
250011506

prune584.0ms

Filtered
162 candidates to 103 candidates (63.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.3b

localize26.0ms

Local error

Found 4 expressions with local error:

2.3b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.7b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
5.9b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
19.1b
(* (/ (* (/ 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))))

rewrite232.0ms

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:
2.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
36.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
45.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
136.0ms
(* (/ (* (/ 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))))

series1.9s

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
504.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
397.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
952.0ms
(* (/ (* (/ 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 (25.0ms)

IterNodesCost
011653923
150013194

prune753.0ms

Filtered
220 candidates to 106 candidates (48.2%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 23.8b

localize28.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
2.3b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.7b
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
19.1b
(* (/ (* (/ 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))))

rewrite298.0ms

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:
45.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
2.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
44.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
156.0ms
(* (/ (* (/ 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:
396.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
87.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
514.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
950.0ms
(* (/ (* (/ 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))))

simplify107.0ms

Algorithm
egg-herbie
Counts
490 → 490
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
019609108
150017782

prune777.0ms

Filtered
490 candidates to 121 candidates (24.7%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 20.2b

regimes675.0ms

Accuracy

20.7% (2.2b remaining)

Error of 20.9b against oracle of 18.8b and baseline of 21.5b

bsearch333.0ms

Steps
ItersRangePoint
10
3.94458661202886e+76
9.884633136253305e+89
4.007597097851864e+76
8
-1.9588416456765557e-44
-6.543342778155253e-48
-1.0720133661478495e-44

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05451
15451

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.7s2041×body1280valid
922.0ms1726×body640valid
677.0ms5986×body80valid
288.0ms800×body320valid
121.0ms475×body160valid