Details

sample41.0ms

Algorithm

intervals

Results

18.0ms

287×

body

valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	18
1	116	18
2	329	18
3	935	18
4	2876	18
5	5001	18

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
0.1b	(* (+ (* z 3.13060547623) 11.1667541262) z)
1.7b	(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
22.6b	(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
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` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

12.0ms	(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
7.0ms	(* (+ (* z 3.13060547623) 11.1667541262) z)
15.0ms	(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
27.0ms	(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

series776.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
65.0ms	(* (+ (* z 3.13060547623) 11.1667541262) z)
167.0ms	(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
480.0ms	(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

simplify78.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	573	1240
1	2806	1065
2	5001	1065

prune468.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
0.1b	(* (+ (* z 3.13060547623) 11.1667541262) z)
0.2b	(* y (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
21.5b	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`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`

Counts

4 → 105

Calls

4 calls:

13.0ms	(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
7.0ms	(* (+ (* z 3.13060547623) 11.1667541262) z)
27.0ms	(* y (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
50.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

series788.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
66.0ms	(* (+ (* z 3.13060547623) 11.1667541262) z)
448.0ms	(* y (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
210.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

simplify82.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	593	1919
1	2703	1702
2	5001	1702

prune544.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

5.9b	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
5.9b	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
17.6b	(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
18.8b	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

rewrite116.0ms

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:

12.0ms	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
13.0ms	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
56.0ms	(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
29.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

series977.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
71.0ms	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
467.0ms	(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
368.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

simplify97.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	673	4328
1	2891	3955
2	5001	3822

prune780.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

10.3b	(* (/ y (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
13.5b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
13.5b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
18.8b	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
81×	`sqrt-prod`
80×	`times-frac`
55×	`add-cube-cbrt` `*-un-lft-identity`
33×	`associate-l`
24×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div`
12×	`unswap-sqr`
10×	`pow1`
8×	`sqrt-pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`rem-sqrt-square` `pow1/2` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 174

Calls

4 calls:

56.0ms	(* (/ y (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
12.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
13.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
32.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

series1.6s

Counts

4 → 12

Calls

4 calls:

839.0ms	(* (/ y (sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
122.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
314.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
356.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

simplify109.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	749	5047
1	3269	4581
2	5001	4477

prune1.0s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.5b

regimes668.0ms

Accuracy

97.7% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 27.4b

bsearch148.0ms

Steps

Iters	Range		Point
8	9.346772747760851e+50	5.275745766481616e+53	4.636101799572154e+51
2	-2.319338119088684e+59	-1.9710212454209794e+59	-2.2710920961423764e+59

simplify10.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	26
1	73	26

end0.0ms

sample915.0ms

Algorithm

intervals

Results

584.0ms

8852×

body

valid