Details

sample211.0ms

Algorithm

intervals

Results

97.0ms	1453×	body	80	nan
35.0ms	469×	body	80	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	32	10
1	65	10
2	181	8
3	522	8
4	2203	8
5	5002	8

prune11.0ms

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

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.1b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.7b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod`
10×	`pow1` `add-log-exp`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
3×	`times-frac` `exp-sum` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 95

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series376.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- t 1.0) (log a))
36.0ms	(* y (log z))
111.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
170.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify55.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	492	869
1	2033	708
2	5002	676

prune317.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Merged error: 0.0b

Counts

109 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.1b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.1b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.7b	(/ (* x (* (* (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))) (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-log-exp`
18×	`add-exp-log`
15×	`add-sqr-sqrt` `exp-prod` `*-un-lft-identity` `exp-diff`
14×	`add-cbrt-cube`
12×	`cbrt-div`
10×	`associate-*r/`
9×	`add-cube-cbrt` `exp-sum` `rem-exp-log`
7×	`associate-/l/`
6×	`diff-log` `prod-exp` `cbrt-unprod`
5×	`frac-times` `associate-*l/`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`sub-neg` `times-frac` `associate--l+` `associate-/r*` `sum-log` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
29.0ms	(/ (* x (* (* (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))) (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

series507.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
112.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
112.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
167.0ms	(/ (* x (* (* (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))) (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)

simplify49.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	398	1739
1	1551	1170
2	5001	1027

prune421.0ms

Filtered

101 candidates to 80 candidates (79.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Merged error: 0.0b

Counts

107 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
0.2b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
6.0b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

3180×	`times-frac`
1295×	`add-sqr-sqrt`
1291×	`add-cube-cbrt` `*-un-lft-identity`
793×	`unpow-prod-down`
256×	`exp-sum`
152×	`div-inv`
89×	`associate-/l*`
61×	`sqr-pow`
49×	`add-exp-log`
45×	`div-exp`
26×	`log-prod`
22×	`add-cbrt-cube`
17×	`associate-/r*`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1` `pow-exp`
9×	`cbrt-undiv` `associate-r` `associate-l`
6×	`log-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp`
2×	`pow-flip` `frac-2neg` `log-rec` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `associate-/r/` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 1227

Calls

4 calls:

21.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
5.0ms	(* (log (/ 1 a)) t)
6.0ms	(* y (log (/ 1 z)))
43.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

series877.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))
58.0ms	(* (log (/ 1 a)) t)
40.0ms	(* y (log (/ 1 z)))
492.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

simplify317.0ms

Algorithm

egg-herbie

Counts

1239 → 1239

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5001	34598

prune5.2s

Filtered

1239 candidates to 953 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1237	2	1239
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	1240	5	1245

Merged error: 0b

Counts

1245 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) y)
0.2b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
1.7b	(/ (/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) y) (/ 1 x))

rewrite620.0ms

Algorithm

rewrite-expression-head

Rules

12891×	`times-frac`
4968×	`add-sqr-sqrt`
4964×	`add-cube-cbrt` `*-un-lft-identity`
2392×	`unpow-prod-down`
782×	`exp-sum`
469×	`div-inv`
292×	`associate-/l*`
184×	`sqr-pow`
123×	`div-exp`
122×	`add-exp-log`
34×	`add-cbrt-cube`
26×	`log-prod`
20×	`pow-exp`
18×	`cbrt-undiv`
16×	`associate-/r*`
13×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp`
12×	`pow1`
9×	`associate-r` `associate-l`
6×	`log-pow`
5×	`pow-to-exp`
4×	`add-log-exp`
2×	`pow-flip` `frac-2neg` `log-rec` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `associate-/r/` `distribute-rgt-neg-out`

Counts

4 → 3524

Calls

4 calls:

28.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) y)
5.0ms	(* (log (/ 1 a)) t)
7.0ms	(* y (log (/ 1 z)))
119.0ms	(/ (/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) y) (/ 1 x))

series1.1s

Counts

4 → 12

Calls

4 calls:

520.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) y)
56.0ms	(* (log (/ 1 a)) t)
43.0ms	(* y (log (/ 1 z)))
500.0ms	(/ (/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) y) (/ 1 x))

simplify1.0s

Algorithm

egg-herbie

Counts

3536 → 3536

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5576	118511

prune17.0s

Filtered

3536 candidates to 2720 candidates (76.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	3536	0	3536
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	3536	5	3541

Merged error: 0b

Counts

3541 → 5

regimes268.0ms

Accuracy

76% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 1.4b

bsearch354.0ms

Steps

Iters	Range		Point
7	2.6533129134673643e-115	4.432324946191695e-114	5.04326216364718e-115
8	-1.9957591474050248e+71	-1.091826104599258e+67	-2.3318989978962595e+68

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.0s	45888×	body	80	nan
1.2s	15245×	body	80	valid

Details

sample211.0ms

simplify53.0ms

prune11.0ms

localize19.0ms

rewrite33.0ms

series376.0ms

simplify55.0ms

prune317.0ms

localize24.0ms

rewrite53.0ms

series507.0ms

simplify49.0ms

prune421.0ms

localize22.0ms

rewrite203.0ms

series877.0ms

simplify317.0ms

prune5.2s

localize26.0ms

rewrite620.0ms

series1.1s

simplify1.0s

prune17.0s

regimes268.0ms

bsearch354.0ms

simplify2.0ms

end0.0ms

sample6.5s

Profiling