Details

sample343.0ms

Algorithm

intervals

Results

27.0ms	52×	body	10240	exit
20.0ms	302×	body	80	nan
18.0ms	255×	body	80	valid
0.0ms	1×	body	320	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	315	5
5	1609	5
6	5001	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

3.0ms	(pow (sqrt (atan2 b b)) (- b a))
4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series105.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow (sqrt (atan2 b b)) (- b a))
60.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms	(sqrt (atan2 b b))

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	148	325
1	425	298
2	1346	292
3	5001	290

prune123.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (/ (- b a) 2))
0.2b	(sin (pow (atan2 b b) (/ (- b a) 2)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow-unpow`
18×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `unpow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `div-sub` `pow-exp` `div-inv` `pow-sub` `sqr-pow`

Counts

2 → 41

Calls

2 calls:

4.0ms	(pow (atan2 b b) (/ (- b a) 2))
3.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

series80.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(pow (atan2 b b) (/ (- b a) 2))
60.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

simplify72.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	232	319
1	750	303
2	3077	285
3	5001	284

prune117.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(/ 1 (* (cbrt 2) (cbrt 2)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
12×	`pow1`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `pow-flip` `*-un-lft-identity` `pow1/3`
7×	`add-cbrt-cube`
4×	`div-exp` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `inv-pow`

Counts

4 → 68

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
7.0ms	(/ 1 (* (cbrt 2) (cbrt 2)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(/ 1 (* (cbrt 2) (cbrt 2)))

simplify79.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (75.0ms)

Iter	Nodes	Cost
0	128	266
1	384	230
2	970	201
3	2429	200
4	5002	195

prune183.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- b a)) (cbrt (- b a)))
0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

20.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
2.0ms	(cbrt (- b a))
2.0ms	(cbrt (- b a))
2.0ms	(cbrt (- b a))

series558.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
141.0ms	(cbrt (- b a))
145.0ms	(cbrt (- b a))
148.0ms	(cbrt (- b a))

simplify152.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (144.0ms)

Iter	Nodes	Cost
0	261	760
1	914	723
2	4499	670
3	5001	660

prune360.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

regimes38.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample2.5s

Algorithm

intervals

Results

988.0ms	1864×	body	10240	exit
603.0ms	9960×	body	80	nan
563.0ms	7992×	body	80	valid
9.0ms	3×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid