Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

265×

body

valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	6
1	67	6
2	145	6
3	241	6
4	301	6
5	355	6
6	396	6
7	444	6
8	529	6
9	744	6
10	2218	6
11	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 18.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ t1 u) (+ t1 u))
17.7b	(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

505×	`*-un-lft-identity`
380×	`times-frac`
295×	`add-sqr-sqrt`
294×	`associate-l`
211×	`add-cube-cbrt`
147×	`associate-r`
126×	`swap-sqr` `distribute-lft-out`
63×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
42×	`*-commutative` `unswap-sqr`
21×	`neg-mul-1`
20×	`associate-/r*`
19×	`associate-/l*`
16×	`add-exp-log` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
9×	`pow1`
8×	`frac-times` `associate-/r/`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
2×	`+-commutative` `distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u` `add-log-exp`
1×	`distribute-lft-neg-out` `pow2` `frac-2neg` `pow-plus` `distribute-frac-neg` `pow-prod-down` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

2 → 492

Calls

2 calls:

8.0ms	(* (+ t1 u) (+ t1 u))
29.0ms	(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

series103.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(* (+ t1 u) (+ t1 u))
82.0ms	(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

simplify87.0ms

Algorithm

egg-herbie

Counts

498 → 498

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1505	4781
1	5002	4610

prune455.0ms

Filtered

498 candidates to 211 candidates (42.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	491	7	498
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	491	8	499

Merged error: 0.0b

Counts

499 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ t1 (+ t1 u))
0.0b	(/ v (+ t1 u))
2.2b	(* (/ v (+ t1 u)) (- (/ t1 (+ t1 u))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

168×	`*-un-lft-identity`
110×	`distribute-neg-frac`
100×	`frac-times`
96×	`associate-/r*`
95×	`add-sqr-sqrt`
90×	`add-cube-cbrt`
72×	`associate-/l*`
61×	`times-frac`
40×	`associate-r`
39×	`distribute-lft-out`
24×	`frac-2neg` `clear-num`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l`
12×	`add-exp-log` `add-cbrt-cube`
10×	`associate-r/` `associate-l/` `associate-/r/`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`neg-mul-1` `pow-prod-down` `*-commutative` `distribute-rgt-neg-out`

Counts

3 → 266

Calls

3 calls:

5.0ms	(/ t1 (+ t1 u))
5.0ms	(/ v (+ t1 u))
31.0ms	(* (/ v (+ t1 u)) (- (/ t1 (+ t1 u))))

series127.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ t1 (+ t1 u))
25.0ms	(/ v (+ t1 u))
61.0ms	(* (/ v (+ t1 u)) (- (/ t1 (+ t1 u))))

simplify53.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1055	1894
1	5002	1792

prune318.0ms

Filtered

275 candidates to 162 candidates (58.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	270	5	275
Fresh	6	0	6
Picked	0	1	1
Done	1	0	1
Total	277	6	283

Merged error: 0b

Counts

283 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ t1 u))
0.6b	(cbrt (+ t1 u))
0.6b	(cbrt (+ t1 u))
1.6b	(/ (- (/ v (* (cbrt (+ t1 u)) (cbrt (+ t1 u))))) (* (cbrt (+ t1 u)) (/ (+ t1 u) t1)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

16470×	`times-frac`
11016×	`*-un-lft-identity`
10249×	`add-sqr-sqrt`
6447×	`add-cube-cbrt`
6114×	`cbrt-prod`
4929×	`associate-r`
3564×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2940×	`associate-l`
2085×	`distribute-lft-out`
1791×	`swap-sqr`
1680×	`unswap-sqr`
824×	`cbrt-div`
569×	`associate-/r/`
420×	`*-commutative`
415×	`flip3-+` `flip-+`
288×	`frac-times` `div-inv`
237×	`associate-/l*`
144×	`associate-*r/`
134×	`associate-*l/`
73×	`associate-/r*`
44×	`associate-/l/`
38×	`distribute-neg-frac`
33×	`neg-mul-1`
18×	`add-cbrt-cube`
13×	`add-exp-log`
7×	`cbrt-undiv`
6×	`clear-num`
5×	`frac-2neg`
4×	`pow1` `expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `un-div-inv`
2×	`prod-exp`
1×	`neg-sub0` `div-sub` `distribute-frac-neg`

Counts

4 → 7441

Calls

4 calls:

3.0ms	(cbrt (+ t1 u))
3.0ms	(cbrt (+ t1 u))
3.0ms	(cbrt (+ t1 u))
205.0ms	(/ (- (/ v (* (cbrt (+ t1 u)) (cbrt (+ t1 u))))) (* (cbrt (+ t1 u)) (/ (+ t1 u) t1)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (+ t1 u))
132.0ms	(cbrt (+ t1 u))
132.0ms	(cbrt (+ t1 u))
92.0ms	(/ (- (/ v (* (cbrt (+ t1 u)) (cbrt (+ t1 u))))) (* (cbrt (+ t1 u)) (/ (+ t1 u) t1)))

simplify1.7s

Algorithm

egg-herbie

Counts

7453 → 7453

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	7284	195702

prune16.1s

Filtered

7453 candidates to 4409 candidates (59.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	7453	0	7453
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	7453	6	7459

Merged error: 0b

Counts

7459 → 6

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ v (+ t1 u))
2.2b	(/ (- (/ v (+ t1 u))) (/ (+ t1 u) t1))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

1552×	`times-frac`
1094×	`*-un-lft-identity`
632×	`add-sqr-sqrt` `add-cube-cbrt`
306×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
231×	`distribute-lft-out`
82×	`associate-/r/`
77×	`div-inv`
50×	`associate-/l*`
36×	`flip3-+` `flip-+`
27×	`associate-/r*`
17×	`neg-mul-1`
12×	`associate-/l/`
10×	`distribute-neg-frac`
9×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`neg-sub0` `div-sub` `distribute-frac-neg`

Counts

2 → 771

Calls

2 calls:

5.0ms	(/ v (+ t1 u))
30.0ms	(/ (- (/ v (+ t1 u))) (/ (+ t1 u) t1))

series88.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ v (+ t1 u))
62.0ms	(/ (- (/ v (+ t1 u))) (/ (+ t1 u) t1))

simplify159.0ms

Algorithm

egg-herbie

Counts

777 → 777

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	2865	10580
1	5002	10386

prune1.1s

Filtered

777 candidates to 456 candidates (58.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	776	1	777
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	777	6	783

Merged error: 0b

Counts

783 → 6

regimes94.0ms

Accuracy

55.4% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 1.5b

bsearch59.0ms

Steps

Iters	Range		Point
7	1.6642112851005508e-17	6.707335497444815e-16	2.5797567822584585e-16
7	-1.8347284548271936e+73	-2.541648319617525e+71	-2.205791074229281e+72

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	24
1	60	24
2	66	24
3	69	24
4	81	24
5	81	24

end0.0ms

sample388.0ms

Algorithm

intervals

Results

220.0ms

8228×

body

valid