Details

sample23.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify49.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
0.0b	(- (* y z) x)
0.3b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
9.9b	(/ (- (* y z) x) (- (* t z) x))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

37.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
8.0ms	(- (* y z) x)
124.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
28.0ms	(/ (- (* y z) x) (- (* t z) x))

series252.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
19.0ms	(- (* y z) x)
106.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
53.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify61.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	455	1085
1	1987	1003
2	5001	1002

prune296.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
2.2b	(/ y (- (* t z) x))
2.3b	(/ x (- (* t z) x))
3.6b	(fma (/ y (- (* t z) x)) z x)

rewrite42.0ms

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:

11.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
15.0ms	(/ y (- (* t z) x))
13.0ms	(/ x (- (* t z) x))
0.0ms	(fma (/ y (- (* t z) x)) z x)

series209.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
25.0ms	(/ y (- (* t z) x))
55.0ms	(/ x (- (* t z) x))
48.0ms	(fma (/ y (- (* t z) x)) z x)

simplify48.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (39.0ms)

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

prune330.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
2.2b	(/ y (- (* t z) x))
2.3b	(/ x (- (* t z) x))
3.6b	(fma (/ y (- (* t z) x)) z x)

rewrite39.0ms

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:

11.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
13.0ms	(/ y (- (* t z) x))
13.0ms	(/ x (- (* t z) x))
0.0ms	(fma (/ y (- (* t z) x)) z x)

series202.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
25.0ms	(/ y (- (* t z) x))
53.0ms	(/ x (- (* t z) x))
49.0ms	(fma (/ y (- (* t z) x)) z x)

simplify43.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (34.0ms)

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

prune322.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (- (* t z) x))
2.3b	(/ x (- (* t z) x))
2.3b	(* y (/ 1 (- (* t z) x)))
3.6b	(fma (* y (/ 1 (- (* t z) x))) z x)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`associate-r`
13×	`add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/r/` `associate-/l`
5×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `associate-l` `flip--` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 116

Calls

4 calls:

18.0ms	(/ 1 (- (* t z) x))
13.0ms	(/ x (- (* t z) x))
35.0ms	(* y (/ 1 (- (* t z) x)))
0.0ms	(fma (* y (/ 1 (- (* t z) x))) z x)

series147.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1 (- (* t z) x))
50.0ms	(/ x (- (* t z) x))
29.0ms	(* y (/ 1 (- (* t z) x)))
46.0ms	(fma (* y (/ 1 (- (* t z) x))) z x)

simplify52.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	353	722
1	1547	634
2	5002	608

prune351.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes196.0ms

Accuracy

8.9% (4.0b remaining)

Error of 4.2b against oracle of 0.3b and baseline of 4.6b

bsearch72.0ms

Steps

Iters	Range		Point
8	-2.9291728540359864e-303	-3.8284825051561105e-306	-1.0874360737987293e-304
4	-7.372919433586017e-21	-4.045822494560777e-21	-4.329769589365412e-21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	38
1	52	38
2	52	38

end0.0ms

sample594.0ms

Algorithm

intervals

Results

304.0ms

8348×

body

valid