Details

Time bar (total: 16.9s)

sample131.0ms

Algorithm
intervals
Results
47.0ms58×body1280valid
31.0ms59×body640valid
20.0ms180×body80valid
13.0ms35×body320valid
3.0ms13×body160valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
04813
116113
294413
3500212

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.7b

localize21.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (pow t 3.0) (sin k))
3.3b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
4.8b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
25.7b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite53.0ms

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))
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))))

series1.4s

Counts
4 → 12
Calls
4 calls:
173.0ms
(* (pow t 3.0) (sin k))
322.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
72.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
865.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify51.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010192396
150011978

prune757.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.1b

localize21.0ms

Local error

Found 4 expressions with local error:

2.6b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
2.9b
(* (pow t 3.0) (sin k))
6.4b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
16.2b
(* (/ (* (/ 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:
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)
45.0ms
(* (/ (* (/ 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:
448.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
172.0ms
(* (pow t 3.0) (sin k))
335.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
871.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify119.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09131905
148941506
250011506

prune783.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.5b

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.6b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
6.4b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
16.2b
(* (/ (* (/ 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))))

rewrite226.0ms

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)))
35.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
43.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
133.0ms
(* (/ (* (/ 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:
86.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
492.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
382.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
913.0ms
(* (/ (* (/ 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))))

simplify64.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011653923
150013194

prune749.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 21.5b

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.6b
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
3.0b
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
16.2b
(* (/ (* (/ (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))))

rewrite287.0ms

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)))
44.0ms
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
51.0ms
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
164.0ms
(* (/ (* (/ (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))))

series2.3s

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
644.0ms
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
519.0ms
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
1.1s
(* (/ (* (/ (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))))

simplify84.0ms

Algorithm
egg-herbie
Counts
313 → 313
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015406709
150015373

prune939.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 17.3b

regimes857.0ms

Accuracy

0% (2.7b remaining)

Error of 21.9b against oracle of 19.2b and baseline of 21.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03323
13323

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2018×body1280valid
937.0ms1724×body640valid
685.0ms5947×body80valid
336.0ms853×body320valid
113.0ms428×body160valid