Details

sample27.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

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: 18.9b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite39.0ms

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)
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series479.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
65.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
50.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
123.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify68.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (14.0ms)

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

prune239.0ms

Filtered

90 candidates to 63 candidates (70.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 0.0b

Counts

91 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

14.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.2b	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-exp-log`
24×	`associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`cbrt-prod` `cbrt-div`
18×	`add-cbrt-cube`
15×	`associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 108

Calls

4 calls:

7.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
40.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

series440.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
105.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
105.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
121.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

simplify89.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	678	2226
1	3162	1944
2	5001	1833

prune448.0ms

Filtered

120 candidates to 101 candidates (84.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	119	7	126

Merged error: 0.0b

Counts

126 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

9.3b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
13.8b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.8b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

40.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
48.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
50.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
118.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify90.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	720	2535
1	3084	2327
2	5001	2242

prune447.0ms

Filtered

162 candidates to 116 candidates (71.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	162	7	169

Merged error: 0.0b

Counts

169 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

14.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
18.1b	(* (/ (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (cbrt (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
113×	`add-sqr-sqrt`
78×	`cbrt-div`
74×	`cbrt-prod`
72×	`associate-l`
50×	`add-cube-cbrt` `*-un-lft-identity`
42×	`associate-/r/`
36×	`add-exp-log`
34×	`flip3-+` `flip-+`
33×	`associate-r`
22×	`add-cbrt-cube`
21×	`frac-times`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
11×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
6×	`pow1` `div-inv`
4×	`add-log-exp`
3×	`pow1/3`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 192

Calls

4 calls:

6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
79.0ms	(* (/ (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (cbrt (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
107.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
103.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
119.0ms	(* (/ (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (cbrt (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1235	6308
1	5002	5913

prune1.0s

Filtered

204 candidates to 187 candidates (91.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	204	7	211

Merged error: 0.0b

Counts

211 → 7

regimes215.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.8b

bsearch201.0ms

Steps

Iters	Range		Point
9	39972.03059165128	205171415297.0802	766133.7099284258
11	-7.015238773634505e+25	-1032953.8864155973	-2128773.026593912

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	28
1	57	28

end0.0ms

sample624.0ms

Algorithm

intervals

Results

449.0ms

8000×

body

valid

Details

sample27.0ms

simplify64.0ms

prune3.0ms

localize15.0ms

rewrite39.0ms

series479.0ms

simplify68.0ms

prune239.0ms

localize20.0ms

rewrite63.0ms

series440.0ms

simplify89.0ms

prune448.0ms

localize18.0ms

rewrite74.0ms

series339.0ms

simplify90.0ms

prune447.0ms

localize25.0ms

rewrite113.0ms

series438.0ms

simplify88.0ms

prune1.0s

regimes215.0ms

bsearch201.0ms

simplify2.0ms

end0.0ms

sample624.0ms

Profiling