Details

Time bar (total: 17.5s)

sample189.0ms

Algorithm
intervals
Results
65.0ms59×body1280valid
49.0ms62×body640valid
29.0ms172×body80valid
20.0ms38×body320valid
4.0ms11×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04813
116113
294413
3500212

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.0b

localize20.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow t 3.0) (sin k))
3.8b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
5.9b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
22.5b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite57.0ms

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
(* (pow t 3.0) (sin k))
8.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
3.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
29.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series368.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (pow t 3.0) (sin k))
75.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
23.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
233.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010192396
150011978

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.8b

localize19.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow t 3.0) (sin k))
3.0b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
6.5b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
15.3b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite81.0ms

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))
11.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
13.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
45.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (pow t 3.0) (sin k))
111.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
79.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
231.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify110.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09131905
148941506
250011506

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.8b

localize28.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.0b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
6.5b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
15.3b
(* (/ (* (/ 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))))

rewrite234.0ms

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))
44.0ms
(* (/ 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))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
122.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
89.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
243.0ms
(* (/ (* (/ 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))))

simplify57.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011653923
150013194

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.9b

localize29.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.4b
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
3.0b
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
15.3b
(* (/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
756×add-exp-log
368×prod-exp
302×div-exp
196×add-cbrt-cube
84×cbrt-unprod
70×cbrt-undiv
68×pow-exp
55×times-frac
45×add-sqr-sqrt
44×pow-to-exp
42×associate-*l*
40×add-cube-cbrt *-un-lft-identity
15×sqrt-prod
14×associate-*r*
11×pow1
7×associate-*l/
6×unpow-prod-down associate-/r* sqr-pow
5×div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×frac-times associate-*r/ associate-/l/
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative unswap-sqr
Counts
4 → 301
Calls
4 calls:
2.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
52.0ms
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
47.0ms
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
168.0ms
(* (/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series502.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
96.0ms
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
133.0ms
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
246.0ms
(* (/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify76.0ms

Algorithm
egg-herbie
Counts
313 → 313
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015406709
150015373

prune2.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.1b

regimes1.0s

Accuracy

23.5% (2.0b remaining)

Error of 20.8b against oracle of 18.8b and baseline of 21.4b

bsearch190.0ms

Steps
ItersRangePoint
6
8.328761947950547e-38
1.2745856103065608e-36
1.2515289756445332e-36
7
-1.5189196523935885e+40
-1.2022643258893338e+38
-1.3182669249842476e+38

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05756
15756

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.3s2090×body1280valid
1.3s1682×body640valid
992.0ms5871×body80valid
470.0ms879×body320valid
153.0ms418×body160valid