Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

272×

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

prune3.0ms

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: 24.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* a c) (* b d))
24.3b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 47

Calls

2 calls:

4.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* a c) (* b d))
84.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify91.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	244	458
1	872	411
2	3164	403
3	5001	403

prune150.0ms

Filtered

53 candidates to 44 candidates (83.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	46	7	53
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	8	54

Merged error: 15.3b

Counts

54 → 8

localize11.0ms

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))
14.9b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

5.0ms	(/ 1 (* (hypot c d) 1))
14.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
1.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series389.0ms

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))
114.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify49.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	486	1199
1	1655	892
2	5001	884

prune248.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	151	6	157
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	155	10	165

Merged error: 6.2b

Counts

165 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.3b	(fma a c (* b d))
14.9b	(/ (fma a c (* b d)) (hypot c d))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`prod-exp` `associate-/r*` `div-inv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

9.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
1.0ms	(fma a c (* b d))
3.0ms	(/ (fma a c (* b d)) (hypot c d))

series271.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
38.0ms	(fma a c (* b d))
117.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify87.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670

prune235.0ms

Filtered

98 candidates to 76 candidates (77.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	97	11	108

Merged error: 6.1b

Counts

108 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.3b	(fma a c (* b d))
15.0b	(/ (hypot c d) (fma a c (* b d)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

260×	`times-frac`
124×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
81×	`add-exp-log`
50×	`div-exp` `associate-/l*`
32×	`add-cbrt-cube`
17×	`associate-/r*`
16×	`cbrt-undiv`
15×	`1-exp` `div-inv`
14×	`prod-exp`
8×	`rec-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/r/` `cbrt-unprod`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 246

Calls

4 calls:

13.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
6.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
1.0ms	(fma a c (* b d))
3.0ms	(/ (hypot c d) (fma a c (* b d)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
117.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
37.0ms	(fma a c (* b d))
92.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify86.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	795	2590
1	3687	2260
2	5001	2098

prune457.0ms

Filtered

258 candidates to 142 candidates (55.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	256	2	258
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	259	10	269

Merged error: 6.1b

Counts

269 → 10

regimes229.0ms

Accuracy

30.6% (7.7b remaining)

Error of 13.5b against oracle of 5.8b and baseline of 16.9b

bsearch54.0ms

Steps

Iters	Range		Point
4	2.717020015622849e+106	5.180485946024502e+106	3.304152526622725e+106
7	-8.589742672742014e+234	-4.780849313130469e+232	-9.349443594143428e+232

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	30	14
2	30	14

end0.0ms

sample597.0ms

Algorithm

intervals

Results

370.0ms

8480×

body

valid