Details

sample70.0ms

Algorithm

intervals

Results

54.0ms	132×	body	10240	exit
6.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	5
1	7	5

prune2.0ms

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: 1.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
1.2b	(/ (exp a) (+ (exp a) (exp b)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 53

Calls

2 calls:

4.0ms	(+ (exp a) (exp b))
7.0ms	(/ (exp a) (+ (exp a) (exp b)))

series55.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (exp a) (exp b))
33.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify106.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	172	409
1	531	381
2	1310	379
3	4468	378
4	5001	378

prune137.0ms

Filtered

59 candidates to 44 candidates (74.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	54	5	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	5	60

Merged error: 0.9b

Counts

60 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- a (log (+ (exp a) (exp b)))))
0.0b	(+ (exp a) (exp b))
1.5b	(- a (log (+ (exp a) (exp b))))
3.8b	(log (+ (exp a) (exp b)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `prod-diff`
16×	`exp-sum`
13×	`pow1` `add-log-exp`
12×	`log-prod`
9×	`log-pow`
8×	`associate--r+`
6×	`log-div` `exp-prod`
5×	`add-exp-log` `exp-diff`
4×	`expm1-log1p-u` `flip3-+` `diff-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `associate--r-`
3×	`fma-def` `fma-neg` `rem-exp-log`
2×	`sub-neg` `difference-of-squares`
1×	`+-commutative` `flip3--` `rem-log-exp` `sum-log` `flip--`

Counts

4 → 112

Calls

4 calls:

10.0ms	(exp (- a (log (+ (exp a) (exp b)))))
4.0ms	(+ (exp a) (exp b))
8.0ms	(- a (log (+ (exp a) (exp b))))
5.0ms	(log (+ (exp a) (exp b)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(exp (- a (log (+ (exp a) (exp b)))))
18.0ms	(+ (exp a) (exp b))
36.0ms	(- a (log (+ (exp a) (exp b))))
34.0ms	(log (+ (exp a) (exp b)))

simplify98.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	318	1374
1	816	989
2	3017	822
3	5001	722

prune272.0ms

Filtered

124 candidates to 74 candidates (59.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	125	4	129

Merged error: 0.9b

Counts

129 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.2b	(log (exp (exp (- a (log (+ (exp a) (exp b)))))))
1.5b	(- a (log (+ (exp a) (exp b))))
3.8b	(log (+ (exp a) (exp b)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
28×	`log-pow`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `prod-diff`
19×	`exp-prod`
16×	`exp-sum`
13×	`pow1`
11×	`log-prod`
9×	`add-log-exp`
6×	`add-exp-log` `log-div`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `associate--r+` `associate--r-`
3×	`fma-def` `fma-neg` `rem-log-exp` `distribute-lft-out`
2×	`sub-neg` `diff-log` `distribute-lft-out--`
1×	`+-commutative` `flip3--` `sum-log` `flip--` `difference-of-squares`

Counts

4 → 107

Calls

4 calls:

5.0ms	(+ (exp a) (exp b))
8.0ms	(log (exp (exp (- a (log (+ (exp a) (exp b)))))))
8.0ms	(- a (log (+ (exp a) (exp b))))
5.0ms	(log (+ (exp a) (exp b)))

series135.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (exp a) (exp b))
47.0ms	(log (exp (exp (- a (log (+ (exp a) (exp b)))))))
36.0ms	(- a (log (+ (exp a) (exp b))))
33.0ms	(log (+ (exp a) (exp b)))

simplify89.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	333	1154
1	835	839
2	2786	814
3	5001	684

prune300.0ms

Filtered

119 candidates to 73 candidates (61.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	119	4	123

Merged error: 0.9b

Counts

123 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.3b	(* (sqrt (/ (exp a) (+ (exp a) (exp b)))) (sqrt (/ (exp a) (+ (exp a) (exp b)))))
1.2b	(/ (exp a) (+ (exp a) (exp b)))
1.2b	(/ (exp a) (+ (exp a) (exp b)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

220×	`sqrt-div`
211×	`*-un-lft-identity`
135×	`add-sqr-sqrt`
107×	`add-cube-cbrt`
100×	`frac-times`
98×	`sqrt-prod`
96×	`associate-/r*`
90×	`times-frac`
72×	`associate-/l*`
49×	`distribute-lft-out`
29×	`swap-sqr`
24×	`frac-2neg` `clear-num`
21×	`associate-r` `associate-l`
19×	`pow1`
12×	`add-exp-log` `associate-/r/`
10×	`associate-r/` `associate-l/` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`sqrt-pow1` `pow1/2`
7×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`cbrt-undiv`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 316

Calls

4 calls:

5.0ms	(+ (exp a) (exp b))
33.0ms	(* (sqrt (/ (exp a) (+ (exp a) (exp b)))) (sqrt (/ (exp a) (+ (exp a) (exp b)))))
7.0ms	(/ (exp a) (+ (exp a) (exp b)))
7.0ms	(/ (exp a) (+ (exp a) (exp b)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (exp a) (exp b))
32.0ms	(* (sqrt (/ (exp a) (+ (exp a) (exp b)))) (sqrt (/ (exp a) (+ (exp a) (exp b)))))
37.0ms	(/ (exp a) (+ (exp a) (exp b)))
32.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify93.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	468	4011
1	1879	3747
2	5001	3702

prune614.0ms

Filtered

328 candidates to 163 candidates (49.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	327	1	328
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	328	4	332

Merged error: 0.9b

Counts

332 → 4

regimes102.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	8
1	11	8

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s	3359×	body	10240	exit
205.0ms	8000×	body	80	valid