Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

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: 16.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.4b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.0b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

3.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
19.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series273.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
56.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
119.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify63.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	479	705
1	2236	601
2	5002	601

prune257.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

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:

3.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
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)))
25.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series288.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
120.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
65.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	499	1062
1	2187	948
2	5002	948

prune305.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
12.8b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
12.8b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
12.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite122.0ms

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:

74.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
26.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
52.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
52.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
118.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify84.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	720	2535
1	3084	2327
2	5002	2242

prune646.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

13.3b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
13.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.3b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite20.0ms

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:

5.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
5.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
4.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
5.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series452.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
102.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
105.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
105.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify128.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	376	679
1	1183	635
2	4831	601
3	5001	601

prune342.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes184.0ms

Accuracy

99.4% (0.1b remaining)

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

bsearch134.0ms

Steps

Iters	Range		Point
8	34603714037.68664	1348841620748990.5	35623158844.36978
7	-537794128203271.2	-8723610261783.773	-8854781423687.8

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	20
1	60	20
2	60	20

end0.0ms

sample510.0ms

Algorithm

intervals

Results

342.0ms

8000×

body

valid