Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

331×

body

valid

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	4
1	27	3
2	62	3
3	112	3
4	170	3
5	213	3
6	260	3
7	450	3
8	845	3
9	1532	3
10	3138	3
11	4587	3
12	5001	3

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 1.8b

Counts

2 → 2

localize6.0ms

Local error

Found 1 expressions with local error:

1.7b	(fma (- y x) (/ z t) x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (- y x) (/ z t) x)

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

(fma (- y x) (/ z t) x)

simplify41.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	41	69
1	86	62
2	257	53
3	1248	53
4	5003	53

prune37.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	9	4	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	9	6	15

Merged error: 1.7b

Counts

15 → 6

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (- y x) (/ z t)))
5.2b	(* (- y x) (/ z t))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-r*`
11×	`add-cube-cbrt`
10×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `add-log-exp`
3×	`fma-def`
2×	`expm1-log1p-u` `frac-times` `flip3--` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 56

Calls

2 calls:

3.0ms	(+ x (* (- y x) (/ z t)))
9.0ms	(* (- y x) (/ z t))

series83.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ x (* (- y x) (/ z t)))
47.0ms	(* (- y x) (/ z t))

simplify39.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	306	327
1	1283	301
2	5002	286

prune132.0ms

Filtered

62 candidates to 45 candidates (72.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	6	62
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	60	8	68

Merged error: 0.0b

Counts

68 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (- y x) (* (cbrt (/ z t)) (cbrt (/ z t))))
9.9b	(cbrt (/ z t))
9.9b	(cbrt (/ z t))
9.9b	(cbrt (/ z t))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
29×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
26×	`add-cube-cbrt`
15×	`cbrt-div`
9×	`pow1` `add-exp-log` `frac-times`
7×	`add-cbrt-cube`
6×	`associate-*r/`
5×	`associate-l` `associate-*l/`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv`
1×	`associate-r` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

13.0ms	(* (- y x) (* (cbrt (/ z t)) (cbrt (/ z t))))
2.0ms	(cbrt (/ z t))
2.0ms	(cbrt (/ z t))
2.0ms	(cbrt (/ z t))

series308.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (- y x) (* (cbrt (/ z t)) (cbrt (/ z t))))
62.0ms	(cbrt (/ z t))
58.0ms	(cbrt (/ z t))
63.0ms	(cbrt (/ z t))

simplify90.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	351	805
1	953	733
2	3478	721
3	5001	697

prune325.0ms

Filtered

118 candidates to 93 candidates (78.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	118	8	126

Merged error: 0.0b

Counts

126 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (cbrt (- y x)) (* (cbrt (/ z t)) (cbrt (/ z t))))
9.9b	(cbrt (/ z t))
9.9b	(cbrt (/ z t))
9.9b	(cbrt (/ z t))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

45×	`cbrt-prod`
31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt` `times-frac`
23×	`cbrt-div`
9×	`pow1` `add-exp-log` `frac-times`
8×	`associate-l`
6×	`pow1/3` `associate-*r/`
5×	`pow-prod-down` `associate-*l/` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `div-inv`
2×	`unswap-sqr`
1×	`associate-r` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

14.0ms	(* (cbrt (- y x)) (* (cbrt (/ z t)) (cbrt (/ z t))))
3.0ms	(cbrt (/ z t))
2.0ms	(cbrt (/ z t))
2.0ms	(cbrt (/ z t))

series380.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (cbrt (- y x)) (* (cbrt (/ z t)) (cbrt (/ z t))))
66.0ms	(cbrt (/ z t))
67.0ms	(cbrt (/ z t))
60.0ms	(cbrt (/ z t))

simplify105.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	420	913
1	1068	860
2	3763	847
3	5001	847

prune414.0ms

Filtered

123 candidates to 104 candidates (84.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	122	9	131

Merged error: 0b

Counts

131 → 9

regimes198.0ms

Accuracy

27.3% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 1.7b

bsearch55.0ms

Steps

Iters	Range		Point
4	8.50180759601064e-15	1.300586776622768e-14	1.0331582040161312e-14
7	-1.4348613029384832e-72	-2.924211053040754e-74	-6.1123310519439906e-74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	30	15

end0.0ms

sample558.0ms

Algorithm

intervals

Results

290.0ms

10619×

body

valid