Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

268×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 24.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(- (* b c) (* a d))
24.5b	(/ (- (* b c) (* a 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`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

3 → 64

Calls

3 calls:

4.0ms	(+ (* c c) (* d d))
3.0ms	(- (* b c) (* a d))
8.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
40.0ms	(- (* b c) (* a d))
86.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify41.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	314	555
1	1341	496
2	5001	481

prune209.0ms

Filtered

73 candidates to 59 candidates (80.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	8	74

Merged error: 13.1b

Counts

74 → 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)) (/ (- (* b c) (* a d)) (hypot c d)))
0.7b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log`
38×	`prod-exp`
32×	`add-cbrt-cube`
29×	`div-exp`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`1-exp`
13×	`associate-r`
10×	`cbrt-undiv`
9×	`pow1` `rec-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`flip3--` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

5.0ms	(/ 1 (* (hypot c d) 1))
13.0ms	(* (/ 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))

series384.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (* (hypot c d) 1))
176.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms	(- (* b c) (* a d))
118.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify60.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	553	1211
1	2305	1003
2	5002	995

prune329.0ms

Filtered

155 candidates to 94 candidates (60.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	148	7	155
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	153	10	163

Merged error: 5.3b

Counts

163 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.7b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

1.0ms	(hypot c d)
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))

series315.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot c d)
113.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
41.0ms	(- (* b c) (* a d))
114.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify50.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	458	1435
1	1667	1331
2	5001	1322

prune419.0ms

Filtered

143 candidates to 112 candidates (78.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	4	3	7
Picked	0	1	1
Done	0	2	2
Total	142	11	153

Merged error: 5.2b

Counts

153 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (hypot c d)))
0.7b	(- (* b c) (* a d))
7.4b	(* (/ 1 (sqrt (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
7.6b	(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

rewrite46.0ms

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*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 192

Calls

4 calls:

4.0ms	(/ 1 (sqrt (hypot c d)))
4.0ms	(- (* b c) (* a d))
23.0ms	(* (/ 1 (sqrt (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
7.0ms	(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ 1 (sqrt (hypot c d)))
43.0ms	(- (* b c) (* a d))
115.0ms	(* (/ 1 (sqrt (hypot c d))) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
198.0ms	(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

simplify82.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	671	2149
1	3215	1896
2	5001	1778

prune499.0ms

Filtered

204 candidates to 119 candidates (58.3%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	203	12	215

Merged error: 5.2b

Counts

215 → 12

regimes267.0ms

Accuracy

27.3% (8.6b remaining)

Error of 13.5b against oracle of 4.9b and baseline of 16.7b

bsearch58.0ms

Steps

Iters	Range		Point
5	2.88489180373733e+91	8.703037392267446e+91	7.268592019881047e+91
8	-2.3279684182047428e+238	-3.9326462293102055e+235	-3.978558295461232e+235

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	31	15
2	31	15

end0.0ms

sample501.0ms

Algorithm

intervals

Results

294.0ms

8500×

body

valid