Details

sample259.0ms

Algorithm

intervals

Results

135.0ms	1281×	body	80	nan
56.0ms	405×	body	80	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	17
1	174	17
2	720	17
3	5001	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize32.0ms

Local error

Found 4 expressions with local error:

6.8b	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.9b	(pow (/ d h) (/ 1.0 2.0))
11.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.8b	(pow (/ d l) (/ 1.0 2.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
40×	`pow-exp`
30×	`add-cbrt-cube`
26×	`unpow-prod-down` `pow-unpow`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 190

Calls

4 calls:

14.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
6.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

636.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
67.0ms	(pow (/ d h) (/ 1.0 2.0))
740.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
68.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5001	2125

prune784.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.3b

localize50.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* M D) (* 2.0 d))
6.8b	(* (* (pow (/ d 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)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.9b	(pow (/ d h) (/ 1.0 2.0))
11.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

738×	`add-exp-log`
487×	`prod-exp`
216×	`pow-exp`
171×	`div-exp`
78×	`pow-to-exp`
46×	`add-cbrt-cube`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1` `cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 274

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(* (* (pow (/ d 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)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
6.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* M D) (* 2.0 d))
651.0ms	(* (* (pow (/ d 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)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
68.0ms	(pow (/ d h) (/ 1.0 2.0))
748.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify83.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1780	6072
1	5002	5729

prune867.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.3b

localize52.0ms

Local error

Found 4 expressions with local error:

2.7b	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
4.8b	(/ (* M D) (* 2.0 d))
6.8b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

5483×	`add-exp-log`
4085×	`prod-exp`
1997×	`pow-exp`
1387×	`div-exp`
643×	`pow-to-exp`
232×	`1-exp`
55×	`add-cbrt-cube`
27×	`cbrt-unprod`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 997

Calls

4 calls:

12.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
70.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts

4 → 12

Calls

4 calls:

122.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
35.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
761.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify308.0ms

Algorithm

egg-herbie

Counts

1009 → 1009

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	4197	34505
1	5001	33453

prune947.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 10.4b

localize60.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* M D) (* 2.0 d))
5.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.8b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
7.5b	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

5734×	`add-exp-log`
4256×	`prod-exp`
2022×	`pow-exp`
1445×	`div-exp`
648×	`pow-to-exp`
248×	`1-exp`
75×	`add-cbrt-cube`
40×	`cbrt-unprod`
19×	`associate-r`
16×	`pow1` `rec-exp`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cbrt-undiv`
10×	`times-frac`
7×	`pow-prod-down` `associate-*l/`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-l` `-commutative`
2×	`sub-neg` `div-inv`
1×	`frac-times` `flip3--` `frac-2neg` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l`

Counts

4 → 1034

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
72.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
16.0ms	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

series2.8s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
960.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
998.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))
771.0ms	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

simplify332.0ms

Algorithm

egg-herbie

Counts

1046 → 1046

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	4318	35781
1	5001	34718

prune731.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.3b

regimes1.3s

Accuracy

5.9% (5.9b remaining)

Error of 16.4b against oracle of 10.5b and baseline of 16.8b

bsearch368.0ms

Steps

Iters	Range		Point
8	1.0338094857556896e+27	5.618644324858641e+31	3.1925120038287596e+28
4	-2.920750373954428e-133	-1.755670850222093e-133	-2.0794825451855812e-133

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	120
1	77	120

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.1s	38195×	body	80	nan
1.8s	12716×	body	80	valid