Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

317×

body

valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	25	5
2	41	5
3	63	5
4	80	5
5	96	5
6	113	5
7	121	5
8	124	5
9	124	5

prune5.0ms

Filtered

1 candidates to 0 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: 3.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ y z) (/ t (- 1.0 z)))
0.0b	(/ t (- 1.0 z))
3.1b	(* x (- (/ y z) (/ t (- 1.0 z))))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

1198×	`add-sqr-sqrt`
1194×	`*-un-lft-identity`
1192×	`times-frac`
894×	`add-cube-cbrt`
819×	`prod-diff`
275×	`distribute-rgt-in` `distribute-lft-in`
198×	`frac-sub`
161×	`associate-/r*`
147×	`distribute-lft-out--` `difference-of-squares`
123×	`associate-/l*`
104×	`div-inv`
101×	`associate-*r/`
80×	`associate-/r/`
42×	`flip3--` `flip--`
41×	`frac-2neg` `clear-num`
13×	`fma-neg`
10×	`associate-r`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `sub-neg` `associate-l` `log1p-expm1-u`
1×	`cbrt-undiv` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 1123

Calls

3 calls:

34.0ms	(- (/ y z) (/ t (- 1.0 z)))
6.0ms	(/ t (- 1.0 z))
71.0ms	(* x (- (/ y z) (/ t (- 1.0 z))))

series134.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- (/ y z) (/ t (- 1.0 z)))
38.0ms	(/ t (- 1.0 z))
59.0ms	(* x (- (/ y z) (/ t (- 1.0 z))))

simplify311.0ms

Algorithm

egg-herbie

Counts

1132 → 1132

Iterations

Useful iterations: 1 (64.0ms)

Iter	Nodes	Cost
0	2643	30063
1	5001	27292

prune1.7s

Filtered

1132 candidates to 485 candidates (57.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	1119	13	1132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1120	13	1133

Merged error: 0.2b

Counts

1133 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (- 1.0 z))
0.0b	(/ t (- 1.0 z))
0.2b	(fma y (/ 1 z) (- (/ t (- 1.0 z))))
3.1b	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (/ t (- 1.0 z)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
26×	`add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `associate-/l*`
5×	`fma-udef`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-r` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`cbrt-undiv` `+-commutative` `associate-+l+` `associate-+r+` `flip3--` `frac-2neg` `associate-*r/` `div-exp` `clear-num` `flip--` `div-inv`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

6.0ms	(/ t (- 1.0 z))
6.0ms	(/ t (- 1.0 z))
1.0ms	(fma y (/ 1 z) (- (/ t (- 1.0 z))))
6.0ms	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (/ t (- 1.0 z)))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ t (- 1.0 z))
42.0ms	(/ t (- 1.0 z))
51.0ms	(fma y (/ 1 z) (- (/ t (- 1.0 z))))
106.0ms	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (/ t (- 1.0 z)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	386	1041
1	1562	955
2	5001	946

prune348.0ms

Filtered

131 candidates to 101 candidates (22.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	132	12	144

Merged error: 0b

Counts

144 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* t (/ 1 (- 1.0 z)))
0.2b	(fma y (/ 1 z) (- (/ t (- 1.0 z))))
3.1b	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (* t (/ 1 (- 1.0 z))))))
6.6b	(fma (- (/ t (- 1.0 z))) 1 (* t (/ 1 (- 1.0 z))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
25×	`associate-r`
18×	`add-cube-cbrt`
17×	`times-frac`
15×	`add-exp-log`
13×	`associate-*r/`
11×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `fma-udef`
5×	`prod-exp` `associate-/r*`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u` `associate-/l*` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`un-div-inv` `cbrt-unprod`
2×	`+-commutative` `associate-+l+` `associate-+r+` `div-exp` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative`
1×	`cbrt-undiv` `rec-exp` `flip3--` `frac-2neg` `flip3-+` `1-exp` `flip--` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 109

Calls

4 calls:

13.0ms	(* t (/ 1 (- 1.0 z)))
1.0ms	(fma y (/ 1 z) (- (/ t (- 1.0 z))))
7.0ms	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (* t (/ 1 (- 1.0 z))))))
1.0ms	(fma (- (/ t (- 1.0 z))) 1 (* t (/ 1 (- 1.0 z))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* t (/ 1 (- 1.0 z)))
51.0ms	(fma y (/ 1 z) (- (/ t (- 1.0 z))))
110.0ms	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (* t (/ 1 (- 1.0 z))))))
36.0ms	(fma (- (/ t (- 1.0 z))) 1 (* t (/ 1 (- 1.0 z))))

simplify74.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	496	984
1	2247	868
2	5002	836

prune294.0ms

Filtered

121 candidates to 88 candidates (27.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	121	12	133

Merged error: 0b

Counts

133 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 z))
0.3b	(cbrt (- 1.0 z))
3.1b	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (/ (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))) (cbrt (- 1.0 z))))))
19.5b	(fma (- (/ t (- 1.0 z))) 1 (/ (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))) (cbrt (- 1.0 z))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`fma-udef`
4×	`distribute-rgt-in` `expm1-log1p-u` `cbrt-div` `distribute-lft-in` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`+-commutative` `associate-+l+` `associate-+r+` `flip3--` `pow1/3` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

3.0ms	(cbrt (- 1.0 z))
3.0ms	(cbrt (- 1.0 z))
6.0ms	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (/ (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))) (cbrt (- 1.0 z))))))
1.0ms	(fma (- (/ t (- 1.0 z))) 1 (/ (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))) (cbrt (- 1.0 z))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (- 1.0 z))
101.0ms	(cbrt (- 1.0 z))
104.0ms	(* x (+ (fma y (/ 1 z) (- (/ t (- 1.0 z)))) (fma (- (/ t (- 1.0 z))) 1 (/ (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))) (cbrt (- 1.0 z))))))
36.0ms	(fma (- (/ t (- 1.0 z))) 1 (/ (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))) (cbrt (- 1.0 z))))

simplify52.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	389	1182
1	1440	1074
2	5001	1020

prune274.0ms

Filtered

87 candidates to 71 candidates (18.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	87	12	99

Merged error: 0b

Counts

99 → 12

regimes270.0ms

Accuracy

19.5% (3.7b remaining)

Error of 3.7b against oracle of 0.0b and baseline of 4.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	30
1	43	30

end0.0ms

sample562.0ms

Algorithm

intervals

Results

304.0ms

9993×

body

valid