Details

sample196.0ms

Algorithm

intervals

Results

84.0ms	1533×	body	80	nan
33.0ms	518×	body	80	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	33	10
1	73	10
2	197	8
3	558	8
4	2287	8
5	5001	8

prune10.0ms

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: 0.2b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.0b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

395×	`*-un-lft-identity`
215×	`exp-sum`
192×	`associate-r`
177×	`add-sqr-sqrt`
165×	`times-frac`
161×	`add-cube-cbrt`
135×	`prod-diff`
132×	`associate-l`
96×	`distribute-lft-out`
72×	`log-prod`
70×	`associate--l+`
55×	`associate-/l*`
40×	`distribute-lft-out--`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`associate-+l+` `associate-+r+`
15×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`exp-prod`
10×	`pow1` `add-log-exp`
6×	`*-commutative` `unswap-sqr`
5×	`+-commutative` `sub-neg`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`div-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `pow-prod-down` `associate-*l/` `log-pow` `difference-of-squares`
1×	`flip3--` `frac-2neg` `associate-*r/` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/`

Counts

4 → 366

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
28.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
52.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series383.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
113.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
172.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify145.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1289	5547
1	4884	4154
2	5001	4154

prune926.0ms

Filtered

378 candidates to 185 candidates (48.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	373	5	378
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	374	6	380

Merged error: 0b

Counts

380 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
1.9b	(* (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y) x)

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

1295×	`times-frac`
595×	`add-sqr-sqrt`
571×	`*-un-lft-identity`
570×	`add-cube-cbrt`
445×	`unpow-prod-down`
220×	`associate-l`
178×	`associate-/l*`
140×	`fma-udef`
138×	`exp-sum`
102×	`associate-*l/`
83×	`add-exp-log`
58×	`div-exp`
48×	`associate-/l/`
44×	`div-inv`
35×	`sqr-pow`
18×	`add-cbrt-cube`
16×	`pow-exp`
14×	`prod-exp` `associate-/r*`
7×	`unswap-sqr`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 722

Calls

4 calls:

27.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
65.0ms	(* (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y) x)

series1000.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
84.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
78.0ms	(fma (log (/ 1 a)) t b)
522.0ms	(* (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y) x)

simplify172.0ms

Algorithm

egg-herbie

Counts

734 → 734

Iterations

Useful iterations: 1 (60.0ms)

Iter	Nodes	Cost
0	2712	12135
1	5001	11734

prune3.6s

Filtered

734 candidates to 579 candidates (78.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	730	4	734
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	735	5	740

Merged error: 0b

Counts

740 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
1.0b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
453×	`add-sqr-sqrt`
375×	`*-un-lft-identity`
368×	`add-cube-cbrt`
360×	`associate-r`
301×	`unpow-prod-down`
122×	`associate-/l*`
89×	`fma-udef`
87×	`exp-sum`
83×	`add-exp-log`
48×	`associate-*r/`
46×	`div-exp`
30×	`unswap-sqr`
28×	`div-inv`
27×	`sqr-pow`
26×	`prod-exp` `associate-/l/`
18×	`add-cbrt-cube`
16×	`pow-exp`
15×	`associate-l`
11×	`associate-/r*`
6×	`pow1`
5×	`cbrt-undiv` `clear-num` `*-commutative`
4×	`expm1-log1p-u` `pow-to-exp` `rec-exp` `1-exp` `un-div-inv` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg`
1×	`pow-prod-down`

Counts

4 → 555

Calls

4 calls:

34.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
46.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series830.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
82.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
77.0ms	(fma (log (/ 1 a)) t b)
337.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify140.0ms

Algorithm

egg-herbie

Counts

567 → 567

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2640	10507
1	5002	10159

prune2.5s

Filtered

567 candidates to 413 candidates (72.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	566	1	567
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	567	5	572

Merged error: 0b

Counts

572 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
1.0b	(/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

4086×	`times-frac`
1947×	`add-sqr-sqrt`
1681×	`*-un-lft-identity`
1658×	`add-cube-cbrt`
1224×	`associate-r`
1000×	`unpow-prod-down`
480×	`associate-/r*`
296×	`fma-udef`
294×	`exp-sum`
222×	`associate-/r/`
210×	`add-exp-log`
150×	`div-exp`
120×	`associate-*r/`
102×	`unswap-sqr`
100×	`associate-/l*`
96×	`div-inv`
90×	`sqr-pow`
52×	`prod-exp`
51×	`associate-l`
32×	`pow-exp`
27×	`add-cbrt-cube`
23×	`rec-exp` `1-exp`
17×	`*-commutative`
14×	`clear-num`
12×	`cbrt-undiv`
10×	`un-div-inv`
8×	`pow-to-exp` `frac-2neg`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`remove-double-div`
1×	`pow-flip` `inv-pow`

Counts

4 → 1734

Calls

4 calls:

93.0ms	(/ 1 (/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
41.0ms	(/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

series865.0ms

Counts

4 → 12

Calls

4 calls:

355.0ms	(/ 1 (/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))))
77.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
79.0ms	(fma (log (/ 1 a)) t b)
354.0ms	(/ y (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

simplify394.0ms

Algorithm

egg-herbie

Counts

1746 → 1746

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5001	40764

prune9.4s

Filtered

1746 candidates to 1381 candidates (79.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1744	2	1746
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	1747	4	1751

Merged error: 0b

Counts

1751 → 4

regimes195.0ms

Accuracy

92.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 1.2b

bsearch67.0ms

Steps

Iters	Range		Point
5	9.44842618593397e-10	3.695394219707434e-09	1.1454557351735624e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	28
1	44	28

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.4s	45873×	body	80	nan
959.0ms	15254×	body	80	valid