Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

274×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

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: 25.6b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(+ (* a c) (* b d))
25.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

216×	`*-un-lft-identity`
85×	`distribute-lft-out`
82×	`associate-l`
56×	`times-frac`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`fma-def`
21×	`swap-sqr`
8×	`associate-/r*`
7×	`associate-/l*` `add-log-exp`
6×	`associate-r`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`+-commutative` `sum-log` `associate-/r/` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 151

Calls

3 calls:

17.0ms	(+ (* c c) (* d d))
16.0ms	(+ (* a c) (* b d))
32.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
33.0ms	(+ (* a c) (* b d))
81.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify44.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	301	1060
1	1238	954
2	5001	927

prune281.0ms

Filtered

160 candidates to 81 candidates (50.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	152	9	161

Merged error: 15.8b

Counts

161 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (hypot c d) 1))
0.2b	(* (/ 1 (/ (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.3b	(fma a c (* b d))
15.5b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

571×	`add-sqr-sqrt`
552×	`associate-/r*`
463×	`times-frac`
431×	`*-un-lft-identity`
374×	`add-cube-cbrt`
361×	`frac-times`
170×	`add-exp-log`
138×	`associate-/l*`
133×	`associate-l`
124×	`associate-r`
102×	`unswap-sqr`
93×	`div-exp`
62×	`prod-exp`
50×	`add-cbrt-cube`
46×	`clear-num`
44×	`frac-2neg`
41×	`1-exp`
31×	`div-inv`
28×	`*-commutative`
22×	`associate-/r/`
20×	`cbrt-undiv`
19×	`associate-r/` `associate-l/`
15×	`rec-exp`
13×	`cbrt-unprod`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`un-div-inv` `remove-double-div`
1×	`pow-flip` `pow-prod-down` `fma-udef` `inv-pow`

Counts

4 → 761

Calls

4 calls:

7.0ms	(/ 1 (/ (hypot c d) 1))
62.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
1.0ms	(fma a c (* b d))
8.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series396.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (/ (hypot c d) 1))
182.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
37.0ms	(fma a c (* b d))
121.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify136.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	3091	8405
1	5001	7374

prune1.0s

Filtered

773 candidates to 281 candidates (36.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	763	10	773
Fresh	7	0	7
Picked	1	0	1
Done	0	1	1
Total	771	11	782

Merged error: 5.8b

Counts

782 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.3b	(fma a c (* b d))
15.5b	(/ (fma a c (* b d)) (hypot c d))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*` `associate-/l/`
6×	`div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`hypot-udef` `fma-udef`

Counts

4 → 129

Calls

4 calls:

1.0ms	(hypot c d)
7.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
1.0ms	(fma a c (* b d))
3.0ms	(/ (fma a c (* b d)) (hypot c d))

series316.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot c d)
119.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
36.0ms	(fma a c (* b d))
117.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify95.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	349	1239
1	1132	1149
2	4141	1132
3	5001	1127

prune396.0ms

Filtered

141 candidates to 111 candidates (78.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	140	12	152

Merged error: 5.7b

Counts

152 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma a c (* b d))
0.3b	(* (sqrt (/ 1 (/ (hypot c d) 1))) (/ (* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
6.9b	(/ (* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
8.9b	(* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d)))

rewrite671.0ms

Algorithm

rewrite-expression-head

Rules

3996×	`times-frac`
3400×	`add-sqr-sqrt`
2529×	`*-un-lft-identity`
2287×	`add-cube-cbrt`
2280×	`sqrt-div`
2009×	`associate-/l*`
1892×	`sqrt-prod`
1843×	`frac-times`
1710×	`associate-/r*`
1596×	`associate-l`
437×	`associate-*l/`
432×	`unswap-sqr`
399×	`associate-/l/`
309×	`associate-/r/`
304×	`associate-r`
238×	`div-inv`
171×	`clear-num`
170×	`frac-2neg`
97×	`associate-*r/`
29×	`*-commutative`
20×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv` `fma-udef`
2×	`pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 2790

Calls

4 calls:

1.0ms	(fma a c (* b d))
250.0ms	(* (sqrt (/ 1 (/ (hypot c d) 1))) (/ (* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
39.0ms	(/ (* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
19.0ms	(* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d)))

series876.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma a c (* b d))
181.0ms	(* (sqrt (/ 1 (/ (hypot c d) 1))) (/ (* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
260.0ms	(/ (* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
393.0ms	(* (sqrt (/ 1 (/ (hypot c d) 1))) (fma a c (* b d)))

simplify577.0ms

Algorithm

egg-herbie

Counts

2802 → 2802

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5001	61062

prune7.4s

Filtered

2802 candidates to 1422 candidates (50.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	2802	0	2802
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	2802	12	2814

Merged error: 5.7b

Counts

2814 → 12

regimes276.0ms

Accuracy

37.5% (7.0b remaining)

Error of 12.7b against oracle of 5.7b and baseline of 16.9b

bsearch67.0ms

Steps

Iters	Range		Point
7	3.110085981024015e+154	8.769655940674386e+155	3.997498131334168e+155
7	-1.8864815038392082e+94	-2.1159267475207395e+92	-7.863570656598141e+93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	38	14
2	41	14
3	41	14

end0.0ms

sample530.0ms

Algorithm

intervals

Results

317.0ms

8506×

body

valid