Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	8
1	61	8
2	141	8
3	347	8
4	792	8
5	5002	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
0.9b	(- (* (* z 2.0) z) (* y t))
19.9b	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
5×	`add-cube-cbrt`
3×	`pow1` `cbrt-undiv` `flip3--` `times-frac` `div-exp` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`sub-neg` `diff-log` `associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 51

Calls

3 calls:

58.0ms	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
21.0ms	(- (* (* z 2.0) z) (* y t))
47.0ms	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t))))
34.0ms	(- (* (* z 2.0) z) (* y t))
167.0ms	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

simplify46.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	318	564
1	1519	493
2	5002	493

prune147.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z)))
0.9b	(- (* (* z 2.0) z) (* y t))
5.8b	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
19.3b	(/ (- (* (* z 2.0) z) (* y t)) z)

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
28×	`add-sqr-sqrt` `*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
4×	`pow1` `div-inv` `associate-/l*`
3×	`flip3--` `flip--`
2×	`sub-neg` `frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`div-sub` `associate-/r/` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 102

Calls

4 calls:

44.0ms	(- x (/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z)))
19.0ms	(- (* (* z 2.0) z) (* y t))
34.0ms	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
48.0ms	(/ (- (* (* z 2.0) z) (* y t)) z)

series341.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- x (/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z)))
35.0ms	(- (* (* z 2.0) z) (* y t))
176.0ms	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
48.0ms	(/ (- (* (* z 2.0) z) (* y t)) z)

simplify68.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	472	1105
1	2263	993
2	5002	988

prune294.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (/ (* y 2.0) (- (* 2.0 z) (/ (* t y) z))))
0.0b	(- (* 2.0 z) (/ (* t y) z))
5.1b	(/ (* t y) z)
5.8b	(/ (* y 2.0) (- (* 2.0 z) (/ (* t y) z)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `add-log-exp`
6×	`times-frac` `associate-/r*`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`flip3--` `flip--`
2×	`sub-neg` `frac-2neg` `diff-log` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`distribute-lft-out--` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

32.0ms	(- x (/ (* y 2.0) (- (* 2.0 z) (/ (* t y) z))))
10.0ms	(- (* 2.0 z) (/ (* t y) z))
10.0ms	(/ (* t y) z)
22.0ms	(/ (* y 2.0) (- (* 2.0 z) (/ (* t y) z)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- x (/ (* y 2.0) (- (* 2.0 z) (/ (* t y) z))))
41.0ms	(- (* 2.0 z) (/ (* t y) z))
17.0ms	(/ (* t y) z)
164.0ms	(/ (* y 2.0) (- (* 2.0 z) (/ (* t y) z)))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	332	566
1	1474	506
2	5002	506

prune183.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 2.0 z) (* t (/ y z)))
0.0b	(- x (/ (* y 2.0) (- (* 2.0 z) (* t (/ y z)))))
5.8b	(/ (* y 2.0) (- (* 2.0 z) (* t (/ y z))))
6.3b	(* t (/ y z))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
13×	`times-frac` `associate-r`
8×	`add-log-exp`
6×	`pow1`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-l` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`sub-neg` `diff-log` `associate-/r/` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 81

Calls

4 calls:

8.0ms	(- (* 2.0 z) (* t (/ y z)))
24.0ms	(- x (/ (* y 2.0) (- (* 2.0 z) (* t (/ y z)))))
22.0ms	(/ (* y 2.0) (- (* 2.0 z) (* t (/ y z))))
14.0ms	(* t (/ y z))

series288.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* 2.0 z) (* t (/ y z)))
62.0ms	(- x (/ (* y 2.0) (- (* 2.0 z) (* t (/ y z)))))
167.0ms	(/ (* y 2.0) (- (* 2.0 z) (* t (/ y z))))
18.0ms	(* t (/ y z))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	395	614
1	1802	554
2	5001	554

prune206.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

regimes157.0ms

Accuracy

-12.1% (2.3b remaining)

Error of 2.8b against oracle of 0.5b and baseline of 2.5b

bsearch91.0ms

Steps

Iters	Range		Point
8	1.529348907157365e-298	5.392511489534144e-296	3.8725642139486444e-297
7	-2.6295099999438543e-217	-1.807249532923465e-219	-7.171100663984459e-219

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	41	16
2	41	16

end0.0ms

sample574.0ms

Algorithm

intervals

Results

299.0ms

8000×

body

valid