Details

Time bar (total: 32.4s)

sample130.0ms

Algorithm
intervals
Results
51.0ms65×body1280valid
26.0ms50×body640valid
19.0ms178×body80valid
12.0ms33×body320valid
6.0ms24×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (765.0ms)

IterNodesCost
01925
14725
215625
379125
4393424
done500024

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.7b

localize22.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (/ (pow t 3.0) (* l l)) (sin k))
2.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.2b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
15.6b
(/ (pow t 3.0) (* l l))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
59×times-frac add-cbrt-cube
49×prod-exp
43×div-exp
39×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
21×cbrt-unprod
19×cbrt-undiv
17×associate-/l*
16×associate-*l/
12×associate-*l* associate-/r/
11×pow1
10×tan-quot unpow-prod-down
8×pow-to-exp pow-exp
7×div-inv
6×associate-*r*
5×frac-times associate-*r/
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u add-log-exp unswap-sqr sqr-pow
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 178
Calls
4 calls:
15.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
36.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
48.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
247.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
320.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
630.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
181.0ms
(/ (pow t 3.0) (* l l))

simplify1.3s

Counts
190 → 190
Iterations

Useful iterations: 2 (554.0ms)

IterNodesCost
03714464
19894301
238873731
done50013731

prune723.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.3b

localize29.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.5b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.2b
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
333×add-exp-log
157×prod-exp
132×div-exp
103×times-frac
88×add-cbrt-cube
72×add-sqr-sqrt
59×add-cube-cbrt *-un-lft-identity
46×associate-*l/
36×cbrt-unprod
35×associate-*l*
33×pow-exp
29×cbrt-undiv
28×associate-/r/
25×frac-times
24×unpow-prod-down
22×pow-to-exp
20×tan-quot
19×associate-/l*
15×pow1 associate-*r/
10×cbrt-prod
8×sqr-pow
7×pow-prod-down div-inv
6×associate-*r* associate-/r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 266
Calls
4 calls:
81.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
22.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
108.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
366.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
242.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
196.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
702.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify664.0ms

Counts
278 → 278
Iterations

Useful iterations: done (653.0ms)

IterNodesCost
05638511
115818094
done50007950

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 16.3b

localize31.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)))
2.9b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.2b
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite623.0ms

Algorithm
rewrite-expression-head
Rules
1254×add-exp-log
637×div-exp
553×prod-exp
187×add-cbrt-cube
145×pow-to-exp pow-exp
91×times-frac
77×cbrt-unprod
71×cbrt-undiv
64×add-sqr-sqrt
55×associate-*l/
51×add-cube-cbrt *-un-lft-identity
35×associate-*l* associate-/r/
30×frac-times
24×tan-quot
20×unpow-prod-down
18×associate-*r/
17×associate-/l*
15×pow1
10×cbrt-prod
7×pow-prod-down div-inv
6×associate-*r*
5×unswap-sqr
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp sqr-pow
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 416
Calls
4 calls:
177.0ms
(/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)))
177.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
21.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
197.0ms
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.8s

Counts
4 → 12
Calls
4 calls:
512.0ms
(/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)))
363.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
243.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
696.0ms
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify921.0ms

Counts
428 → 428
Iterations

Useful iterations: done (903.0ms)

IterNodesCost
060615669
1185614232
done500012982

prune1.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.4b

localize25.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.7b
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ l (pow (cbrt t) 3.0)))
13.3b
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ l (pow (cbrt t) 3.0))))

rewrite439.0ms

Algorithm
rewrite-expression-head
Rules
3762×times-frac
1415×add-sqr-sqrt
1402×add-cube-cbrt *-un-lft-identity
686×unpow-prod-down
677×add-exp-log
365×div-exp
343×cbrt-prod
337×associate-/r/
328×associate-*l/
327×associate-*r/
262×prod-exp
218×tan-quot
159×div-inv
141×associate-/r*
127×add-cbrt-cube
115×sqr-pow
109×frac-times
68×pow-to-exp pow-exp
59×cbrt-undiv
38×cbrt-unprod
35×associate-*l*
13×associate-/l*
8×pow1
6×associate-*r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative
1×associate-/l/
Counts
4 → 1565
Calls
4 calls:
74.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
23.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.0ms
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ l (pow (cbrt t) 3.0)))
133.0ms
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ l (pow (cbrt t) 3.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
345.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
233.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
334.0ms
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ l (pow (cbrt t) 3.0)))
675.0ms
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ l (pow (cbrt t) 3.0))))

simplify866.0ms

Counts
1577 → 1577
Iterations

Useful iterations: 0 (250.0ms)

IterNodesCost
0262787075
done500087075

prune10.4s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 12.1b

regimes701.0ms

Accuracy

42.2% (1.2b remaining)

Error of 12.5b against oracle of 11.3b and baseline of 13.4b

bsearch384.0ms

Steps
ItersRangePoint
11
3.3923648987972015e-223
4.9068444523282e-195
3.510565307720703e-198
7
-1.3813405654223604e-211
-2.7479110800103385e-213
-3.993168942368029e-212

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
048169
161108
done61108

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.7s2072×body1280valid
929.0ms1742×body640valid
659.0ms5877×body80valid
313.0ms868×body320valid
113.0ms441×body160valid