Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

265×

body

valid

simplify54.0ms

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: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* y z) x)
0.0b	(- (* t z) x)
0.5b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
7.8b	(/ (- (* y z) x) (- (* t z) x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

3.0ms	(- (* y z) x)
3.0ms	(- (* t z) x)
58.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
12.0ms	(/ (- (* y z) x) (- (* t z) x))

series234.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(- (* y z) x)
24.0ms	(- (* t z) x)
125.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
64.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify69.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	462	1042
1	2015	941
2	5001	941

prune380.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
1.7b	(/ y (- (* t z) x))
2.7b	(fma (/ y (- (* t z) x)) z x)
3.4b	(/ x (- (* t z) x))

rewrite18.0ms

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:

5.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
5.0ms	(/ y (- (* t z) x))
0.0ms	(fma (/ y (- (* t z) x)) z x)
5.0ms	(/ x (- (* t z) x))

series249.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
37.0ms	(/ y (- (* t z) x))
58.0ms	(fma (/ y (- (* t z) x)) z x)
63.0ms	(/ x (- (* t z) x))

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	423	735
1	1590	652
2	5001	650

prune401.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma (/ y (- (* t z) x)) z x)
7.5b	(cbrt (- (* t z) x))
7.5b	(cbrt (- (* t z) x))
7.5b	(cbrt (- (* t z) x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

0.0ms	(fma (/ y (- (* t z) x)) z x)
2.0ms	(cbrt (- (* t z) x))
2.0ms	(cbrt (- (* t z) x))
6.0ms	(cbrt (- (* t z) x))

series457.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(fma (/ y (- (* t z) x)) z x)
130.0ms	(cbrt (- (* t z) x))
131.0ms	(cbrt (- (* t z) x))
133.0ms	(cbrt (- (* t z) x))

simplify55.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	203	450
1	517	420
2	1648	400
3	5001	391

prune398.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* y z) x)
0.5b	(/ (+ x (/ (- (* y z) x) (fma t z (- x)))) (+ x 1.0))
7.8b	(/ (- (* y z) x) (fma t z (- x)))

rewrite53.0ms

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-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `prod-diff` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip--` `flip-+` `div-inv`
1×	`associate-+r-` `sub-neg` `fma-neg` `diff-log`

Counts

3 → 93

Calls

3 calls:

3.0ms	(- (* y z) x)
39.0ms	(/ (+ x (/ (- (* y z) x) (fma t z (- x)))) (+ x 1.0))
8.0ms	(/ (- (* y z) x) (fma t z (- x)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(- (* y z) x)
137.0ms	(/ (+ x (/ (- (* y z) x) (fma t z (- x)))) (+ x 1.0))
67.0ms	(/ (- (* y z) x) (fma t z (- x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	395	936
1	1710	858
2	5001	858

prune298.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes230.0ms

Accuracy

24.8% (3.3b remaining)

Error of 3.6b against oracle of 0.3b and baseline of 4.6b

bsearch100.0ms

Steps

Iters	Range		Point
5	4.834384898879693e-20	1.085653884907432e-19	4.8859592844393243e-20
8	-1.9985022556198803e-61	-1.5653644986970318e-64	-1.719877735906631e-63

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	36
1	48	36
2	48	36

end0.0ms

sample554.0ms

Algorithm

intervals

Results

339.0ms

8315×

body

valid