Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

271×

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: 25.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(+ (* a c) (* b d))
25.1b	(/ (+ (* 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))
4.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* 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))
84.0ms	(/ (+ (* 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

prune199.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	9	71

Merged error: 17.5b

Counts

71 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a c (* b d))
0.0b	(/ 1 (* (hypot c d) 1))
0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
17.0b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite32.0ms

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))
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))

series411.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma a c (* b d))
54.0ms	(/ 1 (* (hypot c d) 1))
204.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
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

prune241.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	151	6	157
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	157	9	166

Merged error: 6.0b

Counts

166 → 9

localize10.0ms

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))
17.0b	(/ (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))
7.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
4.0ms	(/ (fma a c (* b d)) (hypot c d))

series274.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify78.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (68.0ms)

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

prune239.0ms

Filtered

98 candidates to 76 candidates (77.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	96	11	107

Merged error: 5.9b

Counts

107 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (* (hypot c d) 1)))
0.3b	(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
6.9b	(/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
10.2b	(* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`add-exp-log` `associate-l` `add-cbrt-cube`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
12×	`pow1`
10×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
5×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-pow1` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-l/` `associate-/r`
2×	`pow-flip` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `frac-times` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-r/` `clear-num` `associate-/l/` `associate-/l` `inv-pow`

Counts

4 → 117

Calls

4 calls:

4.0ms	(sqrt (/ 1 (* (hypot c d) 1)))
15.0ms	(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
11.0ms	(/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
9.0ms	(* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (/ 1 (* (hypot c d) 1)))
184.0ms	(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d)))
269.0ms	(/ (* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d))) (hypot c d))
174.0ms	(* (sqrt (/ 1 (* (hypot c d) 1))) (fma a c (* b d)))

simplify70.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	469	1373
1	2225	1115
2	5002	1054

prune340.0ms

Filtered

129 candidates to 99 candidates (76.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	129	11	140

Merged error: 5.9b

Counts

140 → 11

regimes180.0ms

Accuracy

37.6% (6.9b remaining)

Error of 12.8b against oracle of 5.9b and baseline of 16.9b

bsearch51.0ms

Steps

Iters	Range		Point
9	6.706292609373229e+140	6.496812129054123e+149	3.2090803209596246e+146
2	-4.517665970254472e+175	-3.982587382927654e+175	-4.3170115000069156e+175

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

sample502.0ms

Algorithm

intervals

Results

292.0ms

8472×

body

valid