Details

analyze505.0ms

Algorithm: search

sample22.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify62.0ms

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: 22.7b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.5b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
21.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
9.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
14.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series48.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
13.0ms	(* 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))

simplify71.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	525	728
1	2508	623
2	5001	623

prune155.0ms

Filtered

68 candidates to 100 candidates (-47.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
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)))
16.1b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `associate-l`
5×	`flip3-+` `flip-+`
4×	`associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-*r/` `clear-num` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

8.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
15.0ms	(* 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))

series40.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (+ z 6.012459259764103) z)
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))

simplify69.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	545	1085
1	2456	970
2	5002	970

prune179.0ms

Filtered

84 candidates to 118 candidates (-40.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	118	5	123

Merged error: 0.0b

Counts

123 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

11.6b	(* (/ 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))))
16.0b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.0b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.0b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite61.0ms

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:

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))))
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))

series48.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (/ 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))))
8.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify88.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	701	2328
1	3188	2046
2	5001	1935

prune396.0ms

Filtered

101 candidates to 120 candidates (-18.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	5	125

Merged error: 0.0b

Counts

125 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ z 6.012459259764103))
0.7b	(* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103)))
4.5b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
21.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103))) (* (cbrt (+ z 6.012459259764103)) z)) 3.350343815022304))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
28×	`cbrt-prod`
27×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
14×	`cbrt-div`
13×	`pow1` `add-exp-log`
11×	`add-cbrt-cube`
10×	`flip3-+` `associate-r` `associate-l` `flip-+`
9×	`swap-sqr`
7×	`pow1/3` `distribute-lft-out`
6×	`associate-*r/`
5×	`unswap-sqr`
4×	`frac-times` `add-log-exp`
3×	`times-frac` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-/r/` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-plus` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 114

Calls

4 calls:

3.0ms	(cbrt (+ z 6.012459259764103))
10.0ms	(* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103)))
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
29.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103))) (* (cbrt (+ z 6.012459259764103)) z)) 3.350343815022304))

series53.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ z 6.012459259764103))
11.0ms	(* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103)))
12.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
24.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (* (cbrt (+ z 6.012459259764103)) (cbrt (+ z 6.012459259764103))) (* (cbrt (+ z 6.012459259764103)) z)) 3.350343815022304))

simplify85.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	698	1390
1	2951	1227
2	5001	1177

prune269.0ms

Filtered

84 candidates to 126 candidates (-50.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	126	5	131

Merged error: 0.0b

Counts

131 → 5

regimes221.0ms

Accuracy

97.8% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 15.9b

bsearch184.0ms

Steps

Iters	Range		Point
7	2.0461382726038497e-09	3.782620507735315e-08	3.734066881849974e-08
6	-2815062625.6050076	-230010248.32071313	-263957269.41459128

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	19
1	53	19

end0.0ms

analyze501.0ms

Algorithm: search

sample602.0ms

Algorithm

intervals

Results

440.0ms

8000×

body

valid

Details

analyze505.0ms

sample22.0ms

simplify62.0ms

prune3.0ms

localize14.0ms

rewrite37.0ms

series48.0ms

simplify71.0ms

prune155.0ms

localize14.0ms

rewrite46.0ms

series40.0ms

simplify69.0ms

prune179.0ms

localize19.0ms

rewrite61.0ms

series48.0ms

simplify88.0ms

prune396.0ms

localize18.0ms

rewrite55.0ms

series53.0ms

simplify85.0ms

prune269.0ms

regimes221.0ms

bsearch184.0ms

simplify2.0ms

end0.0ms

analyze501.0ms

sample602.0ms

Profiling