Details

sample33.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	10
1	64	10
2	143	10
3	288	10
4	443	10
5	563	10
6	648	10
7	817	10
8	1060	10
9	1066	10
10	1066	10

prune3.0ms

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: 20.2b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.4b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-*r/`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `div-inv` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

4.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
9.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series45.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
12.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
24.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	479	705
1	2236	601
2	5002	601

prune134.0ms

Filtered

63 candidates to 90 candidates (-42.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	4	91

Merged error: 0.0b

Counts

91 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r/`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-*r/` `clear-num` `sum-log`

Counts

4 → 96

Calls

4 calls:

4.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
16.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
13.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series39.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
24.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify61.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	499	1062
1	2187	948
2	5003	948

prune167.0ms

Filtered

80 candidates to 108 candidates (-35.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Merged error: 0.0b

Counts

112 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.9b	(* y (* (+ (* z 0.0692910599291889) 0.4917317610505968) z))
19.4b	(/ (+ (* y (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* y 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

4.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
7.0ms	(* y (* (+ (* z 0.0692910599291889) 0.4917317610505968) z))
15.0ms	(/ (+ (* y (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* y 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series44.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
11.0ms	(* y (* (+ (* z 0.0692910599291889) 0.4917317610505968) z))
23.0ms	(/ (+ (* y (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)) (* y 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify59.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	463	897
1	1992	792
2	5001	790

prune137.0ms

Filtered

70 candidates to 98 candidates (-40.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	98	4	102

Merged error: 0.0b

Counts

102 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

7.2b	(/ (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
8.5b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.2b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.2b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-div`
18×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
13×	`associate-/l*`
12×	`flip3-+` `associate-/r*` `flip-+`
9×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod`

Counts

4 → 170

Calls

4 calls:

22.0ms	(/ (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
5.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series66.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
31.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
4.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify94.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	757	3402
1	3170	3066
2	5001	3056

prune362.0ms

Filtered

114 candidates to 182 candidates (-59.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	182	4	186

Merged error: 0.0b

Counts

186 → 4

regimes185.0ms

Accuracy

98% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 16.1b

bsearch35.0ms

Steps

Iters	Range		Point
5	102488356.31035754	318970690.0289946	104230107.00093396
9	-1.4264057025842507e+66	-1.7250965555295064e+57	-1.7704488784677663e+57

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	20
1	55	20

end0.0ms

sample669.0ms

Algorithm

intervals

Results

413.0ms

8000×

body

valid

Details

sample33.0ms

simplify58.0ms

prune3.0ms

localize13.0ms

rewrite38.0ms

series45.0ms

simplify61.0ms

prune134.0ms

localize13.0ms

rewrite41.0ms

series39.0ms

simplify61.0ms

prune167.0ms

localize14.0ms

rewrite34.0ms

series44.0ms

simplify59.0ms

prune137.0ms

localize16.0ms

rewrite55.0ms

series66.0ms

simplify94.0ms

prune362.0ms

regimes185.0ms

bsearch35.0ms

simplify2.0ms

end0.0ms

sample669.0ms

Profiling