Details

sample29.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	10
1	79	10
2	210	10
3	483	10
4	910	10
5	1516	10
6	2818	10
7	5001	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
0.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.9b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
29.0b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (+ x y) z)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
15.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series755.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ x y) z)
51.0ms	(+ (* (+ x y) z) (* (+ t y) a))
98.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
585.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify70.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	568	1186
1	2526	1087
2	5001	1076

prune372.0ms

Filtered

117 candidates to 93 candidates (79.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 9.1b

Counts

118 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (fma x z (* z y)) (* (+ t y) a))
1.0b	(fma x z (* z y))
2.9b	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
29.0b	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
12×	`distribute-lft-out`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `prod-diff` `associate-/l*`
2×	`flip3--` `flip3-+` `diff-log` `sum-log` `associate-/r/` `flip--` `flip-+` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `associate-+l+` `frac-2neg` `div-sub` `div-exp` `associate--l+` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

4.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
1.0ms	(fma x z (* z y))
5.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
11.0ms	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series426.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
31.0ms	(fma x z (* z y))
104.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
234.0ms	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify51.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	368	1067
1	1651	987
2	5001	975

prune290.0ms

Filtered

103 candidates to 77 candidates (74.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	103	11	114

Merged error: 9.1b

Counts

114 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
0.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.9b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
29.1b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
10×	`associate-*l/`
7×	`pow1` `flip3-+` `flip-+`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `frac-add` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `associate-l` `prod-diff` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `diff-log` `1-exp` `sum-log` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `fma-def` `frac-2neg` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 133

Calls

4 calls:

7.0ms	(/ 1 (+ (+ x t) y))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
19.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series797.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1 (+ (+ x t) y))
51.0ms	(+ (* (+ x y) z) (* (+ t y) a))
100.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
589.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	606	1370
1	2954	1192
2	5001	1143

prune350.0ms

Filtered

145 candidates to 94 candidates (64.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	144	12	156

Merged error: 9.1b

Counts

156 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* (+ t y) a) (* y b))
9.2b	(/ (/ (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y)))
9.4b	(/ (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y)))
10.2b	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y)))

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

6336×	`times-frac`
6316×	`*-un-lft-identity`
3975×	`cbrt-prod`
2385×	`distribute-lft-out`
2341×	`add-sqr-sqrt` `add-cube-cbrt`
279×	`associate-/l*`
186×	`cbrt-div` `associate-/r/`
93×	`flip3-+` `flip-+` `div-inv`
24×	`associate-/r*`
20×	`add-exp-log`
10×	`cbrt-undiv` `div-exp` `add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--`

Counts

4 → 2607

Calls

4 calls:

6.0ms	(- (* (+ t y) a) (* y b))
92.0ms	(/ (/ (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y)))
21.0ms	(/ (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y)))
8.0ms	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y)))

series3.8s

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* (+ t y) a) (* y b))
437.0ms	(/ (/ (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y)))
2.0s	(/ (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y))) (cbrt (+ (+ x t) y)))
1.4s	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (cbrt (+ (+ x t) y)))

simplify779.0ms

Algorithm

egg-herbie

Counts

2619 → 2619

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	3751	92785
1	5001	92145

prune5.8s

Filtered

2619 candidates to 1200 candidates (45.8%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	2616	3	2619
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	2616	15	2631

Merged error: 9.1b

Counts

2631 → 15

regimes597.0ms

Accuracy

47.8% (9.5b remaining)

Error of 17.9b against oracle of 8.4b and baseline of 26.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	30
1	37	30

end0.0ms

sample638.0ms

Algorithm

intervals

Results

381.0ms	7999×	body	80	valid
0.0ms	1×	body	1280	valid