Details

sample41.0ms

Algorithm

intervals

Results

28.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.1b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.0b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite63.0ms

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:

12.0ms	(* (+ z 6.012459259764103) z)
11.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
20.0ms	(* 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))

series273.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ z 6.012459259764103) z)
60.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
53.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
116.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify68.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (14.0ms)

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

prune257.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
12.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
12.6b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
12.6b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite123.0ms

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:

75.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
23.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
10.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series334.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
118.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
51.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
47.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify85.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (62.0ms)

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

prune492.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

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)))
13.2b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite74.0ms

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:

10.0ms	(* (+ z 6.012459259764103) z)
11.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
21.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
26.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series293.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (+ z 6.012459259764103) z)
65.0ms	(* (+ (* 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))

simplify90.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	733	2059
1	3325	1939
2	5001	1937

prune479.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (- 0.08333333333333323 (* 0.0027777777775172263 z)))
0.3b	(* 0.0007936505811533753 (* (pow z 2) y))
4.1b	(+ (* y (- 0.08333333333333323 (* 0.0027777777775172263 z))) (* 0.0007936505811533753 (* (pow z 2) y)))
7.7b	(* (pow z 2) y)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
18×	`add-sqr-sqrt`
14×	`associate-l`
13×	`add-cbrt-cube`
11×	`prod-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
7×	`associate-r`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`distribute-rgt-in` `sub-neg` `unpow-prod-down` `associate-+l+` `distribute-lft-in`
3×	`*-commutative`
2×	`pow-to-exp` `associate-*r/` `pow-prod-down` `pow-exp` `unpow2` `sqr-pow`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+`

Counts

4 → 85

Calls

4 calls:

7.0ms	(* y (- 0.08333333333333323 (* 0.0027777777775172263 z)))
8.0ms	(* 0.0007936505811533753 (* (pow z 2) y))
6.0ms	(+ (* y (- 0.08333333333333323 (* 0.0027777777775172263 z))) (* 0.0007936505811533753 (* (pow z 2) y)))
6.0ms	(* (pow z 2) y)

series159.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* y (- 0.08333333333333323 (* 0.0027777777775172263 z)))
21.0ms	(* 0.0007936505811533753 (* (pow z 2) y))
62.0ms	(+ (* y (- 0.08333333333333323 (* 0.0027777777775172263 z))) (* 0.0007936505811533753 (* (pow z 2) y)))
22.0ms	(* (pow z 2) y)

simplify54.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	334	509
1	1463	444
2	5002	435

prune202.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes104.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.2b

bsearch167.0ms

Steps

Iters	Range		Point
9	0.8894813891870064	5702493.407928515	1326132.872118698
7	-1.5409133811780998e+41	-3.121958070378389e+39	-3.1817420192949543e+39

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	25
1	55	25

end0.0ms

sample952.0ms

Algorithm

intervals

Results

773.0ms

8000×

body

valid