Details

Time bar (total: 17.5s)

sample136.0ms

Algorithm
intervals
Results
52.0ms64×body1280valid
30.0ms57×body640valid
22.0ms200×body80valid
11.0ms29×body320valid
3.0ms13×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04813
116113
294413
3500212

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
3.4b
(* (pow t 3.0) (sin k))
4.1b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
27.2b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite55.0ms

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))
3.0ms
(/ (* 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))))

series1.5s

Counts
4 → 12
Calls
4 calls:
334.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
174.0ms
(* (pow t 3.0) (sin k))
74.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
881.0ms
(* (/ (/ 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 (25.0ms)

IterNodesCost
010192396
150011978

prune780.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.8b

localize20.0ms

Local error

Found 4 expressions with local error:

1.8b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
3.4b
(* (pow t 3.0) (sin k))
6.3b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
19.5b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite82.0ms

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))))

series1.9s

Counts
4 → 12
Calls
4 calls:
460.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
171.0ms
(* (pow t 3.0) (sin k))
353.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
890.0ms
(* (/ (* (/ 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 (24.0ms)

IterNodesCost
09131905
148941506
250011506

prune610.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.4b

localize32.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
1.8b
(/ (* (/ 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)
19.5b
(* (/ (* (/ 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))))

rewrite236.0ms

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)
137.0ms
(* (/ (* (/ 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))))

series2.1s

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
495.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
388.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
1.1s
(* (/ (* (/ 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))))

simplify56.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011653923
150013194

prune712.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.6b

localize30.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)
1.8b
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
1.8b
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
19.5b
(* (/ (* (/ (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))))

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
770×add-exp-log
376×prod-exp
305×div-exp
203×add-cbrt-cube
88×cbrt-unprod
71×cbrt-undiv
69×pow-exp
52×times-frac associate-*l*
45×pow-to-exp
43×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity
18×sqrt-prod
17×associate-*r*
13×pow1
8×associate-*l/
6×unpow-prod-down sqr-pow
5×pow-prod-down div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times associate-*r/ associate-/r* *-commutative associate-/l/ unswap-sqr
2×tan-quot associate-/r/
1×frac-2neg clear-num associate-/l*
Counts
4 → 306
Calls
4 calls:
18.0ms
(* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)
54.0ms
(* (/ (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))
169.0ms
(* (/ (* (/ (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))))

series2.7s

Counts
4 → 12
Calls
4 calls:
450.0ms
(* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)
532.0ms
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
652.0ms
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
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))))

simplify87.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
016266820
150025449

prune889.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 18.5b

regimes681.0ms

Accuracy

21.2% (2.2b remaining)

Error of 21.8b against oracle of 19.6b and baseline of 22.4b

bsearch243.0ms

Steps
ItersRangePoint
7
9.83515075175072e+37
1.9871226502868263e+39
1.312456425802659e+38
5
-3.334217358316846e-62
-1.4280171239812727e-62
-2.690641084259652e-62

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06290
16290

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2067×body1280valid
935.0ms1708×body640valid
699.0ms5909×body80valid
335.0ms886×body320valid
103.0ms406×body160valid