Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

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

localize10.0ms

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)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

4.0ms	(+ (* c c) (* d d))
4.0ms	(+ (* a c) (* b d))
9.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
85.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify135.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462

prune207.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	8	71

Merged error: 15.8b

Counts

71 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
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))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-exp-log`
86×	`prod-exp`
57×	`div-exp`
45×	`add-cbrt-cube`
35×	`1-exp`
16×	`cbrt-unprod`
14×	`cbrt-undiv`
12×	`add-sqr-sqrt` `rec-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`associate-r` `associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
1×	`frac-times` `hypot-udef` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

1.0ms	(hypot c d)
12.0ms	(* (/ 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))

series384.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot c d)
182.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
40.0ms	(fma a c (* b d))
115.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify49.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	486	1106
1	1625	820
2	5001	818

prune275.0ms

Filtered

134 candidates to 72 candidates (53.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	124	10	134
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	130	12	142

Merged error: 5.8b

Counts

142 → 12

localize11.0ms

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

1.0ms	(hypot c d)
10.0ms	(/ (/ (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))

series325.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot c d)
124.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
38.0ms	(fma a c (* b d))
118.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify78.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	308	794
1	1149	701
2	3275	701
3	5001	693

prune325.0ms

Filtered

111 candidates to 89 candidates (80.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	109	14	123

Merged error: 5.7b

Counts

123 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
0.3b	(fma a c (* b d))
6.9b	(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
8.9b	(/ (fma a c (* b d)) (sqrt (hypot c d)))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

5774×	`times-frac`
2456×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1317×	`sqrt-prod`
171×	`div-inv`
99×	`associate-/r*`
50×	`add-exp-log`
34×	`div-exp`
32×	`add-cbrt-cube`
28×	`associate-/l*`
25×	`associate-/r/`
19×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

4 → 1846

Calls

4 calls:

55.0ms	(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
1.0ms	(fma a c (* b d))
8.0ms	(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
5.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
37.0ms	(fma a c (* b d))
160.0ms	(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
198.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

simplify422.0ms

Algorithm

egg-herbie

Counts

1858 → 1858

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5002	48985

prune5.9s

Filtered

1858 candidates to 1213 candidates (65.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	1855	3	1858
Fresh	2	9	11
Picked	1	0	1
Done	0	2	2
Total	1858	14	1872

Merged error: 5.5b

Counts

1872 → 14

regimes308.0ms

Accuracy

36.2% (7.4b remaining)

Error of 12.7b against oracle of 5.3b and baseline of 16.9b

bsearch63.0ms

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	27	14
1	30	14
2	30	14

end0.0ms

sample510.0ms

Algorithm

intervals

Results

293.0ms

8506×

body

valid