Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

269×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	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: 28.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* b c) (* a d))
27.9b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

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

series126.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (* b c) (* a d))
86.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify102.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	268	481
1	1010	432
2	3840	422
3	5001	421

prune133.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	5	57

Merged error: 12.6b

Counts

57 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.2b	(- (* b c) (* a d))
16.6b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`prod-exp`
26×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`rec-exp`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 110

Calls

3 calls:

12.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
4.0ms	(- (* b c) (* a d))
6.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series343.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
39.0ms	(- (* b c) (* a d))
121.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	535	1095
1	2234	907
2	5003	905

prune246.0ms

Filtered

119 candidates to 78 candidates (65.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	8	119
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	114	10	124

Merged error: 5.0b

Counts

124 → 10

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.2b	(- (* b c) (* a d))
16.6b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 121

Calls

3 calls:

7.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
4.0ms	(- (* b c) (* a d))
6.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series284.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
39.0ms	(- (* b c) (* a d))
120.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	449	1408
1	1657	1307
2	5001	1298

prune279.0ms

Filtered

130 candidates to 98 candidates (75.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	129	11	140

Merged error: 5.0b

Counts

140 → 11

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
0.2b	(- (* b c) (* a d))
16.7b	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
14×	`*-un-lft-identity` `times-frac`
13×	`add-cube-cbrt` `associate-r`
9×	`div-exp`
8×	`prod-exp`
6×	`associate-/l/`
5×	`pow1` `cbrt-undiv` `flip3--` `flip--` `add-log-exp`
4×	`frac-times` `associate-*l/` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

3 → 91

Calls

3 calls:

10.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
4.0ms	(- (* b c) (* a d))
9.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

series282.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
45.0ms	(- (* b c) (* a d))
118.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

simplify54.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	408	813
1	1820	677
2	5003	656

prune187.0ms

Filtered

100 candidates to 69 candidates (69.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	100	11	111

Merged error: 5.0b

Counts

111 → 11

regimes265.0ms

Accuracy

16.5% (10.2b remaining)

Error of 14.8b against oracle of 4.5b and baseline of 16.8b

bsearch85.0ms

Steps

Iters	Range	Point
7	7.224436801969521e+81	4.463973393884511e+83	4.407682962117648e+83
8	-6.957313783136581e+63	-1.3416116134587942e+61	-8.901266108273305e+62
3	-2.0986451894772195e+132	-1.711365952199469e+132	-2.0744402371473602e+132

Iters

Range

Point

7.224436801969521e+81

4.463973393884511e+83

4.407682962117648e+83

-6.957313783136581e+63

-1.3416116134587942e+61

-8.901266108273305e+62

-2.0986451894772195e+132

-1.711365952199469e+132

-2.0744402371473602e+132

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	26
1	35	26
2	35	26

end0.0ms

sample509.0ms

Algorithm

intervals

Results

301.0ms

8438×

body

valid