Details

sample80.0ms

Algorithm

intervals

Results

41.0ms

624×

body

valid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	47	14
1	110	13
2	335	13
3	1059	13
4	3442	13
5	5001	13

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 11.7b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i))))
3.8b	(* b (- (* c z) (* t i)))
6.2b	(* j (- (* c a) (* y i)))
6.8b	(* x (- (* y z) (* t a)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-*r/`
19×	`flip3--` `flip--`
17×	`add-sqr-sqrt`
15×	`distribute-rgt-in` `distribute-lft-in`
12×	`frac-add`
11×	`add-cube-cbrt` `sub-neg` `*-un-lft-identity` `prod-diff`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-+l+` `associate-r` `associate-l` `add-log-exp`
8×	`frac-sub`
6×	`associate-+r+` `associate--l+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sum-log`
1×	`+-commutative` `associate-+l-` `flip3-+` `diff-log` `flip-+`

Counts

4 → 129

Calls

4 calls:

14.0ms	(+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i))))
7.0ms	(* b (- (* c z) (* t i)))
6.0ms	(* j (- (* c a) (* y i)))
9.0ms	(* x (- (* y z) (* t a)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

660.0ms	(+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i))))
77.0ms	(* b (- (* c z) (* t i)))
73.0ms	(* j (- (* c a) (* y i)))
81.0ms	(* x (- (* y z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1073	1955
1	5001	1768

prune723.0ms

Filtered

141 candidates to 103 candidates (73.0%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	118	23	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	23	142

Merged error: 5.3b

Counts

142 → 23

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* y z) (* t a))
3.8b	(* b (- (* c z) (* t i)))
5.5b	(fma (- (* c a) (* y i)) j (- (* b (- (* c z) (* t i)))))
6.8b	(* x (- (* y z) (* t a)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `add-log-exp`
5×	`sub-neg` `prod-diff`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log` `fma-udef`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* y z) (* t a))
6.0ms	(* b (- (* c z) (* t i)))
1.0ms	(fma (- (* c a) (* y i)) j (- (* b (- (* c z) (* t i)))))
6.0ms	(* x (- (* y z) (* t a)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* y z) (* t a))
79.0ms	(* b (- (* c z) (* t i)))
245.0ms	(fma (- (* c a) (* y i)) j (- (* b (- (* c z) (* t i)))))
77.0ms	(* x (- (* y z) (* t a)))

simplify64.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	378	597
1	1505	528
2	5002	528

prune671.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	6	16	22
Picked	1	0	1
Done	0	0	0
Total	99	18	117

Merged error: 4.1b

Counts

117 → 18

localize26.0ms

Local error

Found 4 expressions with local error:

2.6b	(fma c (* a j) (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
3.8b	(* b (- (* c z) (* t i)))
5.1b	(* j (- (* y i)))
6.8b	(* x (- (* y z) (* t a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`associate-r`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `prod-diff` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `flip--`
1×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `distribute-rgt-neg-out` `fma-udef`

Counts

4 → 90

Calls

4 calls:

1.0ms	(fma c (* a j) (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
6.0ms	(* b (- (* c z) (* t i)))
5.0ms	(* j (- (* y i)))
6.0ms	(* x (- (* y z) (* t a)))

series766.0ms

Counts

4 → 12

Calls

4 calls:

581.0ms	(fma c (* a j) (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
77.0ms	(* b (- (* c z) (* t i)))
28.0ms	(* j (- (* y i)))
79.0ms	(* x (- (* y z) (* t a)))

simplify84.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	435	635
1	1931	560
2	5001	560

prune476.0ms

Filtered

102 candidates to 78 candidates (76.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	102	18	120

Merged error: 2.5b

Counts

120 → 18

localize31.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
2.3b	(* (cbrt b) (- (* c z) (* t i)))
5.5b	(fma (- (* c a) (* y i)) j (- (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
6.8b	(* x (- (* y z) (* t a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
18×	`distribute-rgt-in` `distribute-lft-in`
15×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
10×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sub-neg` `associate-*r/` `prod-diff`
7×	`associate-r`
4×	`cbrt-prod` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 108

Calls

4 calls:

13.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
7.0ms	(* (cbrt b) (- (* c z) (* t i)))
1.0ms	(fma (- (* c a) (* y i)) j (- (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
6.0ms	(* x (- (* y z) (* t a)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
333.0ms	(* (cbrt b) (- (* c z) (* t i)))
344.0ms	(fma (- (* c a) (* y i)) j (- (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
82.0ms	(* x (- (* y z) (* t a)))

simplify96.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	565	1156
1	2501	916
2	5003	835

prune482.0ms

Filtered

120 candidates to 81 candidates (67.5%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	120	18	138

Merged error: 2.5b

Counts

138 → 18

regimes1.1s

Accuracy

2.1% (10.6b remaining)

Error of 12.7b against oracle of 2.0b and baseline of 12.9b

bsearch117.0ms

Steps

Iters	Range		Point
8	1.9050805902654505e-208	4.552147706951306e-204	1.4987427282522145e-207

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	34
1	76	34
2	77	34
3	77	34

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s

19058×

body

valid