Details

analyze1.8s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 56.579051%

Guaranteed chance to sample good point: 44.444444%

sample45.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
8.0ms	143×	body	80	invalid
4.0ms	73×	body	80	nan

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	41	9
2	88	9
3	165	9
4	287	9
5	625	9
6	2014	9
7	5002	9

prune5.0ms

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: 0.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* t t) 2.0)
0.0b	(exp (/ (* t t) 2.0))
0.0b	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
0.3b	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-cbrt-cube`
14×	`add-exp-log`
13×	`add-sqr-sqrt`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
7×	`exp-prod` `associate-r`
6×	`times-frac` `associate-*l/`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`associate-l` `pow-prod-down`
3×	`associate-/r*`
2×	`cbrt-undiv` `flip3--` `div-exp` `*-commutative` `flip--` `div-inv`
1×	`frac-2neg` `clear-num` `sqrt-prod` `rem-exp-log` `associate-/l*` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

4.0ms	(/ (* t t) 2.0)
2.0ms	(exp (/ (* t t) 2.0))
12.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
8.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (* t t) 2.0)
3.0ms	(exp (/ (* t t) 2.0))
46.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
15.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	413	610
1	1743	532
2	5002	532

prune186.0ms

Filtered

67 candidates to 89 candidates (-32.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 0.0b

Counts

90 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (* t t) 2.0))
0.0b	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
0.3b	(* (- (* x 0.5) y) (sqrt z))
0.4b	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube`
17×	`add-exp-log`
16×	`add-sqr-sqrt`
15×	`associate-r`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`exp-prod` `sqrt-prod`
5×	`associate-l` `add-log-exp`
3×	`flip3--` `times-frac` `*-commutative` `flip--`
2×	`unswap-sqr`
1×	`div-inv` `rem-exp-log`

Counts

4 → 85

Calls

4 calls:

2.0ms	(exp (/ (* t t) 2.0))
14.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
7.0ms	(* (- (* x 0.5) y) (sqrt z))
10.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))

series76.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(exp (/ (* t t) 2.0))
46.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
11.0ms	(* (- (* x 0.5) y) (sqrt z))
16.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	428	794
1	1953	697
2	5001	693

prune174.0ms

Filtered

67 candidates to 97 candidates (-44.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	98	8	106

Merged error: 0.0b

Counts

106 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (exp (/ (* t t) 2.0)))
0.3b	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(* (- (* x 0.5) y) (sqrt z))
0.3b	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1` `add-cbrt-cube`
30×	`add-exp-log`
27×	`associate-r`
22×	`sqrt-prod`
20×	`pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
18×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`flip3--` `*-commutative` `flip--` `add-log-exp`
2×	`unswap-sqr`

Counts

4 → 105

Calls

4 calls:

21.0ms	(* (* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (exp (/ (* t t) 2.0)))
15.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
7.0ms	(* (- (* x 0.5) y) (sqrt z))
11.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (exp (/ (* t t) 2.0)))
16.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
11.0ms	(* (- (* x 0.5) y) (sqrt z))
19.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt (sqrt 2.0)))

simplify78.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	534	1251
1	2692	1017
2	5001	1005

prune223.0ms

Filtered

72 candidates to 117 candidates (-62.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	5	5
Picked	0	1	1
Done	1	1	2
Total	117	8	125

Merged error: 0.0b

Counts

125 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* z 2.0)))
0.1b	(sqrt (sqrt (* z 2.0)))
0.3b	(* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0))))
0.3b	(* (* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0)))) (sqrt (sqrt (* z 2.0))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

21×	`sqrt-prod`
19×	`pow1`
17×	`add-sqr-sqrt`
14×	`associate-r`
12×	`sqrt-pow1`
11×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`pow-prod-down` `associate-*l/`
4×	`pow1/2` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

3.0ms	(sqrt (sqrt (* z 2.0)))
3.0ms	(sqrt (sqrt (* z 2.0)))
10.0ms	(* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0))))
14.0ms	(* (* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0)))) (sqrt (sqrt (* z 2.0))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt (sqrt (* z 2.0)))
20.0ms	(sqrt (sqrt (* z 2.0)))
24.0ms	(* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0))))
14.0ms	(* (* (- (* x 0.5) y) (sqrt (sqrt (* z 2.0)))) (sqrt (sqrt (* z 2.0))))

simplify42.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	382	722
1	1441	629
2	5001	591

prune176.0ms

Filtered

65 candidates to 95 candidates (-46.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	96	7	103

Merged error: 0.0b

Counts

103 → 7

regimes984.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

analyze1.8s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 56.579051%

Guaranteed chance to sample good point: 44.444444%

sample1.4s

Algorithm

intervals

Results

472.0ms	8000×	body	80	valid
320.0ms	5397×	body	80	invalid
138.0ms	2267×	body	80	nan

Details

analyze1.8s

sample45.0ms

simplify78.0ms

prune5.0ms

localize17.0ms

rewrite29.0ms

series67.0ms

simplify49.0ms

prune186.0ms

localize14.0ms

rewrite38.0ms

series76.0ms

simplify57.0ms

prune174.0ms

localize16.0ms

rewrite58.0ms

series92.0ms

simplify78.0ms

prune223.0ms

localize15.0ms

rewrite32.0ms

series77.0ms

simplify42.0ms

prune176.0ms

regimes984.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.8s

sample1.4s

Profiling