Details

sample35.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify61.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 17.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.8b	(/ (* 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:

5.0ms	(* (+ 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))

series46.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ z 6.012459259764103) z)
5.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
14.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
23.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify67.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (14.0ms)

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

prune609.0ms

Filtered

100 candidates to 68 candidates (32.0%)

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: 0b

Counts

101 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
13.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite44.0ms

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)
14.0ms	(* 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))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ z 6.012459259764103) z)
5.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
23.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
5.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify68.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (14.0ms)

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

prune839.0ms

Filtered

118 candidates to 85 candidates (28.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	118	5	123

Merged error: 0b

Counts

123 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (exp (log (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))
0.5b	(exp (log (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
13.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
32×	`log-prod` `exp-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
21×	`associate-r`
10×	`add-cbrt-cube`
9×	`pow1` `add-exp-log`
6×	`associate-l` `associate-/r/`
5×	`flip3-+` `flip-+`
4×	`exp-prod` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`log-div` `exp-diff` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `associate-*r/` `div-exp` `clear-num` `log-pow` `rem-exp-log`

Counts

4 → 115

Calls

4 calls:

7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
17.0ms	(* y (exp (log (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))
12.0ms	(exp (log (/ (+ (* (+ (* 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:

6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
24.0ms	(* y (exp (log (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))
5.0ms	(exp (log (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
5.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify65.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	565	1462
1	2216	1348
2	5001	1327

prune1.2s

Filtered

127 candidates to 97 candidates (23.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	127	5	132

Merged error: 0b

Counts

132 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
12.9b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
12.9b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite58.0ms

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)))
18.0ms	(/ (* 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))

series62.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
28.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
4.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
4.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify92.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (61.0ms)

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

prune1.1s

Filtered

182 candidates to 114 candidates (37.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	182	5	187

Merged error: 0b

Counts

187 → 5

regimes215.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.4b

bsearch155.0ms

Steps

Iters	Range		Point
8	28.700163284045342	1477468.8746106862	671391.3181410683
6	-3.348641433993038e+37	-2.616547962795265e+36	-2.809399130876658e+37

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	19
1	53	19

end0.0ms

sample687.0ms

Algorithm

intervals

Results

415.0ms

8000×

body

valid

Details

sample35.0ms

simplify61.0ms

prune5.0ms

localize13.0ms

rewrite37.0ms

series46.0ms

simplify67.0ms

prune609.0ms

localize13.0ms

rewrite44.0ms

series38.0ms

simplify68.0ms

prune839.0ms

localize17.0ms

rewrite55.0ms

series40.0ms

simplify65.0ms

prune1.2s

localize16.0ms

rewrite58.0ms

series62.0ms

simplify92.0ms

prune1.1s

regimes215.0ms

bsearch155.0ms

simplify2.0ms

end0.0ms

sample687.0ms

Profiling