Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

264×

body

valid

simplify6.0ms

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: 24.0b

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))
23.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

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:

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

simplify139.0ms

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

prune187.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Merged error: 16.6b

Counts

71 → 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))
16.2b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite26.0ms

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:

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

series384.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (* (hypot c d) 1))
179.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
37.0ms	(fma a c (* b d))
115.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify48.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (35.0ms)

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

prune243.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	151	6	157
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	152	13	165

Merged error: 7.0b

Counts

165 → 13

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))
16.2b	(/ (fma a c (* b d)) (hypot c d))

rewrite13.0ms

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:

6.0ms	(/ (/ (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))

series272.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
37.0ms	(fma a c (* b d))
114.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify80.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (70.0ms)

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

prune237.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	4	7	11
Picked	0	1	1
Done	0	1	1
Total	96	15	111

Merged error: 7.0b

Counts

111 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (hypot c d)))
0.3b	(fma a c (* b d))
8.0b	(* (/ 1 (sqrt (hypot c d))) (/ (fma a c (* b d)) (sqrt (hypot c d))))
8.3b	(/ (fma a c (* b d)) (sqrt (hypot c d)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
94×	`times-frac`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 183

Calls

4 calls:

4.0ms	(/ 1 (sqrt (hypot c d)))
1.0ms	(fma a c (* b d))
17.0ms	(* (/ 1 (sqrt (hypot c d))) (/ (fma a c (* b d)) (sqrt (hypot c d))))
4.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 1 (sqrt (hypot c d)))
40.0ms	(fma a c (* b d))
111.0ms	(* (/ 1 (sqrt (hypot c d))) (/ (fma a c (* b d)) (sqrt (hypot c d))))
195.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

simplify73.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	552	1897
1	2733	1667
2	5002	1549

prune371.0ms

Filtered

195 candidates to 111 candidates (56.9%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	3	9	12
Picked	0	1	1
Done	0	2	2
Total	196	14	210

Merged error: 6.0b

Counts

210 → 14

regimes248.0ms

Accuracy

35% (7.4b remaining)

Error of 12.6b against oracle of 5.3b and baseline of 16.6b

bsearch70.0ms

Steps

Iters	Range		Point
10	3.4696428002669553e+165	2.173145948567462e+176	2.2145673082307874e+168
6	-1.8873369306133463e+111	-2.950390700731267e+110	-7.490552277624732e+110

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

sample537.0ms

Algorithm

intervals

Results

312.0ms

8497×

body

valid