Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

273×

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: 29.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.2b	(+ (* a c) (* b d))
28.7b	(/ (+ (* 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)))

series147.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
83.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify134.0ms

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

prune194.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 16.9b

Counts

71 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.3b	(fma a c (* b d))
0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
16.5b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite23.0ms

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)
1.0ms	(fma a c (* b d))
12.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
5.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series395.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot c d)
39.0ms	(fma a c (* b d))
188.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
118.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify48.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (36.0ms)

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

prune245.0ms

Filtered

134 candidates to 72 candidates (53.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	135	9	144

Merged error: 5.2b

Counts

144 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.3b	(fma a c (* b d))
16.5b	(/ (fma a c (* b d)) (hypot c d))

rewrite15.0ms

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)
7.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
1.0ms	(fma a c (* b d))
4.0ms	(/ (fma a c (* b d)) (hypot c d))

series322.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot c d)
117.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
41.0ms	(fma a c (* b d))
115.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify96.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (86.0ms)

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

prune294.0ms

Filtered

111 candidates to 89 candidates (80.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	108	12	120

Merged error: 5.1b

Counts

120 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt (hypot c d)))
0.3b	(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
7.3b	(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
9.4b	(/ (fma a c (* b d)) (sqrt (hypot c d)))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

5792×	`times-frac`
2471×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1329×	`sqrt-prod`
172×	`div-inv`
105×	`associate-/r*`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
31×	`associate-/l*`
25×	`associate-/r/`
20×	`cbrt-undiv`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
1×	`sqrt-pow1` `pow1/2` `associate-/l/` `inv-pow`

Counts

4 → 1883

Calls

4 calls:

7.0ms	(/ 1 (sqrt (hypot c d)))
49.0ms	(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
11.0ms	(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
5.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ 1 (sqrt (hypot c d)))
187.0ms	(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
160.0ms	(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
202.0ms	(/ (fma a c (* b d)) (sqrt (hypot c d)))

simplify456.0ms

Algorithm

egg-herbie

Counts

1895 → 1895

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5001	49275

prune5.3s

Filtered

1895 candidates to 1237 candidates (65.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	1892	3	1895
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	1894	13	1907

Merged error: 4.7b

Counts

1907 → 13

regimes231.0ms

Accuracy

26.5% (8.5b remaining)

Error of 14.2b against oracle of 5.6b and baseline of 17.2b

bsearch66.0ms

Steps

Iters	Range		Point
5	1.3815484546578421e+73	3.4258758800285786e+73	3.3703509945803273e+73
7	-8.813531778917843e+97	-2.645963916783929e+96	-6.678098902910806e+97

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	24
1	38	24
2	38	24

end0.0ms

sample595.0ms

Algorithm

intervals

Results

371.0ms

8488×

body

valid