Details

sample78.0ms

Algorithm

intervals

Results

33.0ms	67×	body	1280	valid
14.0ms	37×	body	640	valid
7.0ms	144×	body	80	valid
6.0ms	30×	body	320	valid
5.0ms	113×	body	80	nan
2.0ms	14×	body	160	valid

simplify119.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 12.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.0b	(/ (pow (/ x (+ x y)) x) x)
7.2b	(pow (/ x (+ x y)) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

5.0ms	(/ x (+ x y))
11.0ms	(/ (pow (/ x (+ x y)) x) x)
7.0ms	(pow (/ x (+ x y)) x)

series405.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ x (+ x y))
136.0ms	(/ (pow (/ x (+ x y)) x) x)
230.0ms	(pow (/ x (+ x y)) x)

simplify72.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	537	1436
1	2640	1406
2	5001	1406

prune336.0ms

Filtered

181 candidates to 131 candidates (72.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Merged error: 0.5b

Counts

182 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`pow1` `cbrt-undiv` `exp-neg` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

4.0ms

(/ (exp (* -1 y)) x)

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(/ (exp (* -1 y)) x)

simplify48.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	114	186
1	303	172
2	1435	169
3	5001	169

prune56.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	31	3	34

Merged error: 0.5b

Counts

34 → 3

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (* x (exp y)))
0.0b	(* x (exp y))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`pow1`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`div-exp` `prod-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `pow-flip` `1-exp` `pow-prod-down` `cbrt-unprod` `add-log-exp`
1×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `div-inv` `inv-pow` `unswap-sqr`

Counts

2 → 46

Calls

2 calls:

5.0ms	(/ 1 (* x (exp y)))
5.0ms	(* x (exp y))

series46.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(/ 1 (* x (exp y)))
21.0ms	(* x (exp y))

simplify94.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	173	200
1	786	167
2	4230	160
3	5002	160

prune57.0ms

Filtered

52 candidates to 28 candidates (53.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	51	4	55

Merged error: 0.5b

Counts

55 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow y 2))
0.0b	(+ (* 1/2 (pow y 2)) (+ y 1))
0.2b	(/ 1 (* x (+ (* 1/2 (pow y 2)) (+ y 1))))
2.8b	(* x (+ (* 1/2 (pow y 2)) (+ y 1)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
19×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`pow1` `add-log-exp`
7×	`prod-exp`
6×	`associate-l`
5×	`unswap-sqr`
4×	`unpow-prod-down` `associate-*r/` `div-exp`
3×	`flip3-+` `times-frac` `sum-log` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `pow-flip` `1-exp` `pow-prod-down` `associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `pow-to-exp` `associate-+r+` `frac-2neg` `distribute-lft-in` `pow-exp` `clear-num` `associate-/r*` `div-inv` `inv-pow`

Counts

4 → 92

Calls

4 calls:

5.0ms	(* 1/2 (pow y 2))
6.0ms	(+ (* 1/2 (pow y 2)) (+ y 1))
9.0ms	(/ 1 (* x (+ (* 1/2 (pow y 2)) (+ y 1))))
8.0ms	(* x (+ (* 1/2 (pow y 2)) (+ y 1)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* 1/2 (pow y 2))
17.0ms	(+ (* 1/2 (pow y 2)) (+ y 1))
50.0ms	(/ 1 (* x (+ (* 1/2 (pow y 2)) (+ y 1))))
40.0ms	(* x (+ (* 1/2 (pow y 2)) (+ y 1)))

simplify68.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	420	654
1	2221	552
2	5001	546

prune140.0ms

Filtered

104 candidates to 62 candidates (59.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	104	4	108

Merged error: 0.5b

Counts

108 → 4

regimes60.0ms

bsearch77.0ms

Steps

Iters	Range		Point
10	-63280.15344050627	-5.037762374958283e-11	-32.7487936042176

Details

sample78.0ms

simplify119.0ms

prune5.0ms

localize6.0ms

rewrite31.0ms

series405.0ms

simplify72.0ms

prune336.0ms

localize4.0ms

rewrite5.0ms

series19.0ms

simplify48.0ms

prune56.0ms

localize4.0ms

rewrite11.0ms

series46.0ms

simplify94.0ms

prune57.0ms

localize9.0ms

rewrite32.0ms

series317.0ms

simplify68.0ms

prune140.0ms

regimes60.0ms

bsearch77.0ms

Profiling