Details

Time bar (total: 1.2m)

sample516.0ms

Algorithm
intervals
Results
291.0ms1295×body80nan
96.0ms441×body80valid

simplify948.0ms

Counts
1 → 1
Iterations
IterNodes
done5001
3710
2174
154
022

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize70.0ms

Local error

Found 4 expressions with local error:

6.3b
(/ M (* 2.0 (/ d D)))
8.7b
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)
10.3b
(pow (/ d h) (/ 1.0 2.0))
12.2b
(pow (/ d l) (/ 1.0 2.0))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
67×add-sqr-sqrt
57×*-un-lft-identity add-cube-cbrt
51×unpow-prod-down
44×add-exp-log
40×associate-*l*
26×pow-unpow
18×add-cbrt-cube
16×div-exp
11×prod-exp
9×div-inv
8×pow1 pow-exp
6×sqr-pow
5×cbrt-undiv
4×associate-*r/ associate-/r/ cbrt-unprod add-log-exp unswap-sqr
3×pow-to-exp associate-*r* associate-/l*
2×pow-pow
1×clear-num associate-/r* frac-2neg pow-prod-down associate-*l/ *-commutative
Counts
4 → 166
Calls
4 calls:
8.0ms
(/ M (* 2.0 (/ d D)))
48.0ms
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)
12.0ms
(pow (/ d h) (/ 1.0 2.0))
14.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ M (* 2.0 (/ d D)))
1.0s
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)
88.0ms
(pow (/ d h) (/ 1.0 2.0))
82.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify2.4s

Counts
178 → 178
Iterations
IterNodes
done5000
24791
11153
0413

prune2.1s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 9.1b

localize79.0ms

Local error

Found 4 expressions with local error:

4.4b
(/ (pow (/ M (* 2.0 (/ d D))) 2.0) l)
6.3b
(/ M (* 2.0 (/ d D)))
8.7b
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)
10.3b
(pow (/ d h) (/ 1.0 2.0))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
78×add-sqr-sqrt
70×unpow-prod-down
68×*-un-lft-identity add-cube-cbrt
58×add-exp-log
40×associate-*l*
25×div-exp
20×add-cbrt-cube
15×associate-/l*
13×pow-unpow prod-exp
12×div-inv
10×pow-exp
9×sqr-pow
8×associate-*r/ associate-/r/
7×pow1
6×cbrt-undiv
4×associate-/r* cbrt-unprod add-log-exp unswap-sqr
3×pow-to-exp associate-*r*
2×clear-num frac-2neg
1×pow-pow pow-prod-down associate-*l/ *-commutative
Counts
4 → 196
Calls
4 calls:
16.0ms
(/ (pow (/ M (* 2.0 (/ d D))) 2.0) l)
13.0ms
(/ M (* 2.0 (/ d D)))
44.0ms
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)
6.0ms
(pow (/ d h) (/ 1.0 2.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
975.0ms
(/ (pow (/ M (* 2.0 (/ d D))) 2.0) l)
57.0ms
(/ M (* 2.0 (/ d D)))
1.0s
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)
117.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify2.1s

Counts
208 → 208
Iterations
IterNodes
done5002
24815
11080
0414

prune3.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.5b

localize133.0ms

Local error

Found 4 expressions with local error:

3.8b
(* (- 1.0 (* (* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0))))
4.4b
(/ (pow (/ M (* 2.0 (/ d D))) 2.0) l)
6.3b
(/ M (* 2.0 (/ d D)))
8.7b
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
169×add-exp-log
99×times-frac
86×prod-exp
65×add-sqr-sqrt
57×unpow-prod-down
55×*-un-lft-identity add-cube-cbrt
47×div-exp
43×associate-*l*
42×pow-exp
25×add-cbrt-cube
15×associate-/l*
13×pow-to-exp
10×div-inv
8×pow1 associate-*r/ associate-/r/ sqr-pow
7×cbrt-unprod
6×cbrt-undiv
4×associate-/r* associate-*r* add-log-exp unswap-sqr
3×associate-*l/
2×clear-num frac-2neg pow-prod-down *-commutative
1×flip3-- flip--
Counts
4 → 204
Calls
4 calls:
103.0ms
(* (- 1.0 (* (* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0))))
22.0ms
(/ (pow (/ M (* 2.0 (/ d D))) 2.0) l)
16.0ms
(/ M (* 2.0 (/ d D)))
55.0ms
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)

series2.9s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (- 1.0 (* (* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0))))
886.0ms
(/ (pow (/ M (* 2.0 (/ d D))) 2.0) l)
35.0ms
(/ M (* 2.0 (/ d D)))
970.0ms
(* (/ (pow (/ M (* 2.0 (/ d D))) 2.0) l) h)

simplify2.1s

Counts
216 → 216
Iterations
IterNodes
done5001
24941
11120
0435

prune3.2s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 7.3b

localize183.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (pow (/ (/ M (/ d D)) 2.0) (/ 2.0 2)) l)
5.6b
(* (/ (pow (/ (/ M (/ d D)) 2.0) (/ 2.0 2)) l) h)
6.3b
(/ M (* 2.0 (/ d D)))
6.3b
(/ M (/ d D))

rewrite686.0ms

Algorithm
rewrite-expression-head
Rules
3240×times-frac
1413×add-sqr-sqrt
1388×*-un-lft-identity add-cube-cbrt
956×unpow-prod-down
424×associate-*l*
146×associate-/l*
99×div-inv
60×add-exp-log
31×div-exp
25×add-cbrt-cube
23×associate-/r/
17×associate-/r*
9×cbrt-undiv prod-exp
8×pow-exp sqr-pow
7×unswap-sqr
6×pow1
4×cbrt-unprod add-log-exp
3×clear-num frac-2neg associate-*r*
2×pow-to-exp
1×pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 1127
Calls
4 calls:
119.0ms
(/ (pow (/ (/ M (/ d D)) 2.0) (/ 2.0 2)) l)
333.0ms
(* (/ (pow (/ (/ M (/ d D)) 2.0) (/ 2.0 2)) l) h)
12.0ms
(/ M (* 2.0 (/ d D)))
13.0ms
(/ M (/ d D))

series2.0s

Counts
4 → 12
Calls
4 calls:
903.0ms
(/ (pow (/ (/ M (/ d D)) 2.0) (/ 2.0 2)) l)
1.0s
(* (/ (pow (/ (/ M (/ d D)) 2.0) (/ 2.0 2)) l) h)
42.0ms
(/ M (* 2.0 (/ d D)))
24.0ms
(/ M (/ d D))

simplify2.3s

Counts
1139 → 1139
Iterations
IterNodes
done5001
14753
02113

prune22.9s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 7.3b

regimes3.4s

Accuracy

4.3% (3.9b remaining)

Error of 11.7b against oracle of 7.8b and baseline of 11.8b

bsearch1.1s

Steps
ItersRangePoint
9
8.050098552876451e-41
4.8151083144102495e-34
8.15097821932325e-41
9
-2.346824376284131e-192
-6.304256451251367e-198
-2.0387893704164653e-193

simplify16.0ms

Iterations
IterNodes
done81
181
062

end0.0ms

sample16.4s

Algorithm
intervals
Results
9.6s37752×body80nan
3.4s12750×body80valid