Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify66.0ms

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: 23.2b

Counts

2 → 1

localize17.0ms

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))
22.4b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite39.0ms

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)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series289.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ z 6.012459259764103) z)
68.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
57.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
121.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify72.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (16.0ms)

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

prune238.0ms

Filtered

100 candidates to 68 candidates (68.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0b

Counts

101 → 4

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)))
19.0b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite50.0ms

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:

6.0ms	(* (+ z 6.012459259764103) z)
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
20.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series502.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ z 6.012459259764103) z)
67.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
119.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
272.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify77.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (15.0ms)

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

prune258.0ms

Filtered

118 candidates to 85 candidates (72.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0b

Counts

122 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.3b	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
19.0b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
64×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`add-cube-cbrt`
18×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r/`
8×	`pow1` `flip3-+` `flip-+`
7×	`associate-l`
6×	`associate-r` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`distribute-lft-out`

Counts

4 → 150

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
15.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
14.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series291.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ z 6.012459259764103) z)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
118.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
64.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify99.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	733	2059
1	3325	1939
2	5002	1937

prune393.0ms

Filtered

162 candidates to 126 candidates (77.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	162	4	166

Merged error: 0b

Counts

166 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.5b	(/ 1 (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
4.5b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
22.5b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
34×	`add-exp-log`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
14×	`div-exp`
12×	`associate-*r/`
11×	`associate-/r/`
10×	`associate-/r*`
9×	`pow1`
8×	`flip3-+` `flip-+`
7×	`cbrt-undiv`
6×	`associate-r` `associate-l` `prod-exp` `div-inv` `associate-/l*`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l/` `unswap-sqr`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `inv-pow`

Counts

4 → 131

Calls

4 calls:

6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
16.0ms	(/ 1 (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
71.0ms	(/ 1 (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
52.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
77.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

simplify103.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	683	1682
1	3506	1467
2	5001	1418

prune248.0ms

Filtered

143 candidates to 81 candidates (56.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	143	4	147

Merged error: 0b

Counts

147 → 4

regimes101.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.0b

bsearch184.0ms

Steps

Iters	Range		Point
11	1.4618569291717553e-22	25.546786954327533	25.24516199592272
8	-2.719453140170837e+30	-4.4361896339540136e+26	-2.6568667296279275e+30

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	19
1	53	19

end0.0ms

sample563.0ms

Algorithm

intervals

Results

395.0ms

8000×

body

valid

Details

sample25.0ms

simplify66.0ms

prune3.0ms

localize17.0ms

rewrite39.0ms

series289.0ms

simplify72.0ms

prune238.0ms

localize14.0ms

rewrite50.0ms

series502.0ms

simplify77.0ms

prune258.0ms

localize13.0ms

rewrite47.0ms

series291.0ms

simplify99.0ms

prune393.0ms

localize15.0ms

rewrite55.0ms

series265.0ms

simplify103.0ms

prune248.0ms

regimes101.0ms

bsearch184.0ms

simplify2.0ms

end0.0ms

sample563.0ms

Profiling