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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.9b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
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` `distribute-lft-out` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

19.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
19.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series447.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
68.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
55.0ms	(* 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))

simplify70.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	534	840
1	2452	738
2	5003	738

prune251.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.2b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.1b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite80.0ms

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:

8.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
37.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
22.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series274.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (* (+ z 6.012459259764103) z) 3.350343815022304)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
125.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
64.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify63.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	504	1086
1	2201	967
2	5001	967

prune303.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

9.1b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
14.5b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.5b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.6b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite114.0ms

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:

72.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
7.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
22.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series352.0ms

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))))
55.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
50.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
124.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify88.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	720	2533
1	3090	2327
2	5002	2242

prune540.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

12.8b	(* (* (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))) y) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.0b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
28×	`associate-*l/`
25×	`add-exp-log`
24×	`associate-r`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-prod` `times-frac` `add-cbrt-cube`
16×	`frac-times` `flip3-+` `flip-+`
13×	`pow1`
12×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow1/3` `div-exp`
2×	`associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

218.0ms	(* (* (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))) y) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
5.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
5.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
5.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series685.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))) y) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
320.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
141.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
152.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify99.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	792	2610
1	3467	2320
2	5001	2204

prune455.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.2b

bsearch139.0ms

Steps

Iters	Range		Point
6	16112908.465778163	243454343.341909	190386035.85313585
10	-2.0648964296169642e+43	-6.322962747029278e+27	-5.542688526226542e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	21
1	48	21

end0.0ms

sample481.0ms

Algorithm

intervals

Results

317.0ms

8000×

body

valid