Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

269×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 29.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(+ (* a c) (* b d))
29.3b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite16.0ms

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))
3.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* c c) (* d d))
33.0ms	(+ (* a c) (* b d))
80.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify135.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

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

prune187.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	10	71

Merged error: 19.1b

Counts

71 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a c (* b d))
0.0b	(/ 1 (* (hypot c d) 1))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
18.8b	(/ (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:

1.0ms	(fma a c (* b d))
5.0ms	(/ 1 (* (hypot c d) 1))
11.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
4.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series385.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma a c (* b d))
55.0ms	(/ 1 (* (hypot c d) 1))
181.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
111.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify47.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884

prune248.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	148	9	157
Fresh	6	2	8
Picked	1	0	1
Done	1	0	1
Total	156	11	167

Merged error: 5.4b

Counts

167 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
18.8b	(/ (fma a c (* b d)) (hypot c d))

rewrite15.0ms

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:

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

series264.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(fma a c (* b d))
114.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
111.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify78.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (69.0ms)

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

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	96	13	109

Merged error: 5.3b

Counts

109 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
18.8b	(/ (hypot c d) (fma a c (* b d)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

264×	`add-exp-log`
162×	`times-frac`
126×	`div-exp`
118×	`prod-exp`
107×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
70×	`1-exp`
52×	`add-cbrt-cube`
46×	`rec-exp`
44×	`associate-r`
21×	`cbrt-undiv`
17×	`associate-/r*`
15×	`pow1`
13×	`cbrt-unprod`
12×	`div-inv`
9×	`associate-/l*`
7×	`pow-flip` `associate-l`
6×	`pow-prod-down`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `inv-pow` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `associate-r/` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 293

Calls

4 calls:

4.0ms	(/ 1 (* (hypot c d) 1))
6.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
21.0ms	(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
3.0ms	(/ (hypot c d) (fma a c (* b d)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (* (hypot c d) 1))
110.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
176.0ms	(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
88.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify90.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	1023	2775
1	3975	2410
2	5001	2207

prune457.0ms

Filtered

305 candidates to 147 candidates (48.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	303	2	305
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	304	14	318

Merged error: 5.3b

Counts

318 → 14

regimes233.0ms

Accuracy

35.6% (7.7b remaining)

Error of 13.2b against oracle of 5.6b and baseline of 17.5b

bsearch63.0ms

Steps

Iters	Range		Point
8	4.5136397962683526e+138	2.0521185469434633e+142	3.200823121324777e+139
6	-2.7039916634838064e+165	-3.519412945082994e+164	-1.1519417024813e+165

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	14
1	31	14
2	31	14

end0.0ms

sample572.0ms

Algorithm

intervals

Results

362.0ms

8425×

body

valid