Details

sample63.0ms

Algorithm

intervals

Results

27.0ms	286×	body	80	valid
7.0ms	100×	body	80	nan

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	176	18
4	422	18
5	1174	18
6	4570	18
done	5000	18

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize29.0ms

Local error

Found 4 expressions with local error:

2.0b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.6b	(/ (* M D) (* 2.0 d))
5.4b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
9.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

31.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
13.0ms	(/ (* M D) (* 2.0 d))
5.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
37.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.0s

Counts

4 → 12

Calls

4 calls:

537.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
39.0ms	(/ (* M D) (* 2.0 d))
478.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
934.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.2s

Counts

125 → 125

Iterations

Useful iterations: 2 (377.0ms)

Iter	Nodes	Cost
0	236	2311
1	577	2083
2	2254	1927
done	5001	1927

prune495.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize23.0ms

Local error

Found 4 expressions with local error:

4.2b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.6b	(/ (* M D) (* 2.0 d))
5.4b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
6.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
21×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac` `cbrt-unprod`
10×	`associate-l`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 128

Calls

4 calls:

54.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
24.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
33.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.3s

Counts

4 → 12

Calls

4 calls:

904.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
46.0ms	(/ (* M D) (* 2.0 d))
486.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
905.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify1.3s

Counts

140 → 140

Iterations

Useful iterations: 2 (513.0ms)

Iter	Nodes	Cost
0	269	2521
1	652	2089
2	2479	1883
done	5000	1883

prune398.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize20.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
4.6b	(/ (* M D) (* 2.0 d))
5.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.4b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
30×	`add-cbrt-cube`
19×	`prod-exp`
14×	`add-sqr-sqrt`
12×	`div-exp`
9×	`associate-l` `cbrt-unprod`
8×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1` `pow-exp`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `sqrt-prod` `div-inv` `unswap-sqr`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--`

Counts

4 → 88

Calls

4 calls:

13.0ms	(/ (* M D) (* 2.0 d))
13.0ms	(/ (* M D) (* 2.0 d))
33.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))

series1.8s

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (* M D) (* 2.0 d))
49.0ms	(/ (* M D) (* 2.0 d))
1.2s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
482.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))

simplify992.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (241.0ms)

Iter	Nodes	Cost
0	171	1908
1	421	1549
2	1797	1317
done	5000	1317

prune469.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize40.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
4.7b	(* (* M D) (/ 1 (* 2.0 d)))
5.1b	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)
5.4b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) (/ 1 l))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-exp-log`
75×	`prod-exp`
39×	`add-cbrt-cube`
20×	`div-exp`
16×	`cbrt-unprod`
15×	`pow-exp`
13×	`add-sqr-sqrt`
10×	`pow1` `associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`associate-l`
4×	`times-frac` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`sqrt-div` `*-commutative` `div-inv` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 112

Calls

4 calls:

19.0ms	(/ (* M D) (* 2.0 d))
59.0ms	(* (* M D) (/ 1 (* 2.0 d)))
34.0ms	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)
8.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) (/ 1 l))))

series1.5s

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (* M D) (* 2.0 d))
39.0ms	(* (* M D) (/ 1 (* 2.0 d)))
933.0ms	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)
517.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) (/ 1 l))))

simplify1.4s

Counts

124 → 124

Iterations

Useful iterations: 2 (615.0ms)

Iter	Nodes	Cost
0	243	2411
1	584	1791
2	2485	1509
done	5000	1509

prune474.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.5b

regimes1.1s

Accuracy

45.3% (1.1b remaining)

Error of 8.6b against oracle of 7.5b and baseline of 9.4b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	37	116
1	52	81
done	52	81

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	9391×	body	80	valid
284.0ms	3020×	body	80	nan