Details

sample40.0ms

Algorithm

intervals

Results

28.0ms

266×

body

valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	8
1	39	8
2	64	8
3	115	8
4	207	8
5	465	8
6	1337	8
7	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* y z) x)
0.3b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
5.8b	(/ (- (* y z) x) (- (* t z) x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
25×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`distribute-lft-out`
7×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`add-log-exp`
4×	`associate-/r/` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `flip3--` `div-sub` `prod-diff` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`associate-+r-` `sub-neg` `fma-neg` `diff-log`

Counts

3 → 95

Calls

3 calls:

4.0ms	(- (* y z) x)
65.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
14.0ms	(/ (- (* y z) x) (- (* t z) x))

series224.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(- (* y z) x)
134.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
67.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify74.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	435	951
1	1923	872
2	5001	872

prune323.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
1.0b	(/ y (- (* t z) x))
1.7b	(/ x (- (* t z) x))
3.1b	(fma (/ y (- (* t z) x)) z x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
15×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`associate-/r*`
6×	`associate-/r/`
5×	`div-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`flip3--` `associate-*l/` `prod-exp` `flip--`
1×	`flip3-+` `1-exp` `cbrt-unprod` `flip-+` `fma-udef`

Counts

4 → 98

Calls

4 calls:

6.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
6.0ms	(/ y (- (* t z) x))
6.0ms	(/ x (- (* t z) x))
1.0ms	(fma (/ y (- (* t z) x)) z x)

series265.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
36.0ms	(/ y (- (* t z) x))
63.0ms	(/ x (- (* t z) x))
65.0ms	(fma (/ y (- (* t z) x)) z x)

simplify58.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	423	735
1	1590	652
2	5002	650

prune407.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (/ (- (* t z) x) y))
1.0b	(/ (- (* t z) x) y)
1.7b	(/ x (- (* t z) x))
3.1b	(fma (/ 1 (/ (- (* t z) x) y)) z x)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
62×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `associate-/r*`
13×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*`
7×	`div-inv`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

4 → 151

Calls

4 calls:

9.0ms	(/ 1 (/ (- (* t z) x) y))
12.0ms	(/ (- (* t z) x) y)
7.0ms	(/ x (- (* t z) x))
1.0ms	(fma (/ 1 (/ (- (* t z) x) y)) z x)

series234.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (/ (- (* t z) x) y))
56.0ms	(/ (- (* t z) x) y)
69.0ms	(/ x (- (* t z) x))
52.0ms	(fma (/ 1 (/ (- (* t z) x) y)) z x)

simplify74.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	508	1180
1	2372	1055
2	5002	983

prune484.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (/ z (- (* t z) x)) y) x) (* (+ x 1.0) 1))
1.7b	(/ x (- (* t z) x))
2.6b	(* (/ z (- (* t z) x)) y)
5.3b	(/ z (- (* t z) x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
31×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log`
18×	`add-cbrt-cube`
15×	`associate-l`
9×	`associate-/l*`
8×	`associate-/r/`
7×	`associate-/r*`
6×	`pow1` `div-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `frac-2neg` `associate-r` `associate-*l/` `clear-num` `flip--` `cbrt-unprod`
2×	`flip3-+` `flip-+` `associate-/l/` `unswap-sqr`
1×	`1-exp` `pow-prod-down` `*-commutative`

Counts

4 → 126

Calls

4 calls:

28.0ms	(/ (+ (* (/ z (- (* t z) x)) y) x) (* (+ x 1.0) 1))
7.0ms	(/ x (- (* t z) x))
18.0ms	(* (/ z (- (* t z) x)) y)
7.0ms	(/ z (- (* t z) x))

series271.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (* (/ z (- (* t z) x)) y) x) (* (+ x 1.0) 1))
65.0ms	(/ x (- (* t z) x))
68.0ms	(* (/ z (- (* t z) x)) y)
35.0ms	(/ z (- (* t z) x))

simplify83.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	561	927
1	2380	825
2	5001	825

prune460.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes188.0ms

Accuracy

45.7% (2.4b remaining)

Error of 2.6b against oracle of 0.2b and baseline of 4.6b

bsearch166.0ms

Steps

Iters	Range		Point
11	1.9380155283280215e+62	2.137254039657746e+83	9.582562178055975e+73
9	-8.871524440761445e+84	-4.6118413363907316e+76	-4.004060635677712e+83

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	23
1	45	23
2	45	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

890.0ms

8331×

body

valid