Details

sample336.0ms

Algorithm

intervals

Results

24.0ms	56×	body	10240	exit
20.0ms	325×	body	80	nan
16.0ms	256×	body	80	valid

simplify57.0ms

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: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.0b	(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:

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

series107.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(pow (sqrt (atan2 b b)) (- b a))
27.0ms	(sqrt (atan2 b b))

simplify45.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	148	325
1	425	298
2	1341	292
3	5001	290

prune125.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`pow1/2` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

4.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
27.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series87.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify53.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	292	1754
1	1319	1646
2	5002	1602

prune348.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)))
0.0b	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

169×	`unpow-prod-down`
133×	`add-sqr-sqrt`
120×	`sqrt-prod`
96×	`cbrt-prod`
65×	`unswap-sqr`
55×	`cube-prod`
39×	`associate-r`
35×	`sqr-pow`
29×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-l`
11×	`add-exp-log`
10×	`unpow-prod-up`
6×	`pow1` `add-cbrt-cube`
5×	`sub-neg` `pow-exp` `pow-sub`
4×	`add-log-exp`
3×	`cube-div` `pow-to-exp` `pow-unpow` `prod-exp`
2×	`cube-mult` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `unpow3`
1×	`frac-times` `pow-pow` `associate-r/` `associate-l/` `*-commutative` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 210

Calls

4 calls:

53.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)))
6.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series109.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)))
50.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3)
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify88.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	450	3134
1	2128	2691
2	5002	2611

prune411.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (exp (* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b)))))))
0.0b	(exp (* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b))))))
0.2b	(* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b)))))
1.0b	(sqrt (atan2 b b))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

39×	`sqrt-prod`
36×	`log-prod`
19×	`add-sqr-sqrt`
18×	`distribute-rgt-in` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in` `exp-sum`
13×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r`
6×	`add-log-exp`
5×	`sqrt-pow1` `log-pow`
3×	`pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-r/` `associate-l/`
1×	`rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `associate-l` `*-commutative` `flip--` `rem-exp-log`

Counts

4 → 91

Calls

4 calls:

14.0ms	(sin (exp (* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b)))))))
13.0ms	(exp (* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b))))))
22.0ms	(* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b)))))
1.0ms	(sqrt (atan2 b b))

series251.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sin (exp (* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b)))))))
29.0ms	(exp (* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b))))))
133.0ms	(* (* 2 (- b a)) (log (sqrt (sqrt (atan2 b b)))))
13.0ms	(sqrt (atan2 b b))

simplify53.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	1078
1	1498	947
2	5001	885

prune215.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms

sample2.3s

Algorithm

intervals

Results

776.0ms	1753×	body	10240	exit
636.0ms	9664×	body	80	nan
469.0ms	7986×	body	80	valid
6.0ms	2×	body	5120	valid
1.0ms	3×	body	640	valid
1.0ms	6×	body	160	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid