Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

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)
3.1b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite41.0ms

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)
7.0ms	(* (+ (* 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))

series308.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (+ z 6.012459259764103) z)
71.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
54.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
132.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify73.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (15.0ms)

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

prune277.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
13.2b	(/ (+ (* (+ (* 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)
17.0ms	(* 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))

series310.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (+ z 6.012459259764103) z)
71.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
131.0ms	(* 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))

simplify73.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	545	1085
1	2456	970
2	5001	970

prune333.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

7.0b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* 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))
12.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite70.0ms

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:

34.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
58.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
57.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
127.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify92.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (68.0ms)

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

prune525.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

13.1b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.1b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
13.1b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
13.1b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
7.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
7.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series562.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
154.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
144.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
149.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify138.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	376	845
1	1183	801
2	4831	723
3	5001	723

prune359.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.8b

bsearch74.0ms

Steps

Iters	Range		Point
2	81461.56837266182	97589.81891588567	95573.78759798268
6	-1398402063.149054	-145619909.40767458	-709774825.8572668

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	19
1	53	19

end0.0ms

sample465.0ms

Algorithm

intervals

Results

306.0ms

8000×

body

valid