Details

sample34.0ms

Algorithm

intervals

Results

22.0ms

267×

body

valid

simplify64.0ms

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: 8.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
0.0b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
11.9b	(/ (- (* y z) x) (- (* t z) x))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

21.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
57.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
12.0ms	(/ (- (* y z) x) (- (* t z) x))

series297.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
139.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
63.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify56.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	398	994
1	1427	934
2	5001	932

prune311.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (- (* t z) x)) (+ x 1.0))
2.4b	(/ x (- (* t z) x))
3.2b	(fma (/ y (- (* t z) x)) z x)
3.3b	(/ y (- (* t z) x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
103×	`*-un-lft-identity`
71×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
16×	`associate-/r/` `distribute-lft-out`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
8×	`div-inv`
7×	`flip3--` `flip--`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`flip3-+` `flip-+` `fma-udef` `associate-/l/`

Counts

4 → 170

Calls

4 calls:

16.0ms	(/ (/ x (- (* t z) x)) (+ x 1.0))
6.0ms	(/ x (- (* t z) x))
0.0ms	(fma (/ y (- (* t z) x)) z x)
6.0ms	(/ y (- (* t z) x))

series508.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(/ (/ x (- (* t z) x)) (+ x 1.0))
69.0ms	(/ x (- (* t z) x))
59.0ms	(fma (/ y (- (* t z) x)) z x)
38.0ms	(/ y (- (* t z) x))

simplify79.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	582	1552
1	2287	1475
2	5002	1475

prune639.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
0.0b	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
0.6b	(/ 1 (- (* t z) x))
11.5b	(* (- (* y z) x) (/ 1 (- (* t z) x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
32×	`times-frac`
30×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`associate-r`
13×	`add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `flip3--` `prod-exp` `flip--` `log1p-expm1-u` `distribute-lft-out`
3×	`cbrt-undiv` `fma-def` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 132

Calls

4 calls:

2.0ms	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
12.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
6.0ms	(/ 1 (- (* t z) x))
24.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
136.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
26.0ms	(/ 1 (- (* t z) x))
65.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	489	1257
1	2101	1127
2	5001	1095

prune398.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
0.1b	(* (+ x (/ (- (* y z) x) (- (* t z) x))) (/ 1 (+ x 1.0)))
11.9b	(/ (- (* y z) x) (- (* t z) x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
35×	`times-frac`
31×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube`
9×	`distribute-lft-out`
7×	`pow1` `associate-/r*`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `flip-+`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `flip3--` `frac-2neg` `1-exp` `div-sub` `associate-*l/` `clear-num` `flip--` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `associate-+r-` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 139

Calls

4 calls:

6.0ms	(/ 1 (+ x 1.0))
18.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
84.0ms	(* (+ x (/ (- (* y z) x) (- (* t z) x))) (/ 1 (+ x 1.0)))
15.0ms	(/ (- (* y z) x) (- (* t z) x))

series315.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (+ x 1.0))
91.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
132.0ms	(* (+ x (/ (- (* y z) x) (- (* t z) x))) (/ 1 (+ x 1.0)))
66.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify81.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	543	1210
1	2408	1092
2	5001	1055

prune406.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes179.0ms

Accuracy

33.2% (2.9b remaining)

Error of 3.2b against oracle of 0.3b and baseline of 4.6b

bsearch248.0ms

Steps

Iters	Range		Point
8	2.596345847547348e+270	9.163179133934984e+273	4.301084569469367e+271
8	3.924373303033543e+253	1.8425873237218792e+258	1.9006882053443136e+254
7	4.9804751387592316e-24	9.250357485506658e-23	8.811735982677568e-23
9	-4.421135035044612e+140	-4.036851611946301e+132	-4.4707659967563265e+138

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	45
1	53	45
2	53	45

end0.0ms

sample915.0ms

Algorithm

intervals

Results

693.0ms

8328×

body

valid