Details

sample233.0ms

Algorithm

intervals

Results

105.0ms	1551×	body	80	nan
43.0ms	503×	body	80	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.8b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.4b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod` `exp-sum`
10×	`pow1` `add-log-exp`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `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 → 112

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
8.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
12.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series382.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- t 1.0) (log a))
41.0ms	(* y (log z))
113.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
168.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify62.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	580	1143
1	2309	897
2	5002	860

prune555.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	121	5	126

Merged error: 0b

Counts

126 → 5

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))))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
7.5b	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

3162×	`times-frac`
1273×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
793×	`unpow-prod-down`
258×	`fma-udef`
256×	`exp-sum`
150×	`div-inv`
89×	`associate-/l*`
61×	`sqr-pow`
45×	`add-exp-log` `div-exp`
18×	`add-cbrt-cube`
17×	`associate-/r*`
12×	`pow-exp`
9×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 1181

Calls

4 calls:

10.0ms	(/ (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)
43.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

series954.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
83.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
77.0ms	(fma (log (/ 1 a)) t b)
504.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

simplify301.0ms

Algorithm

egg-herbie

Counts

1193 → 1193

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5001	30886

prune5.2s

Filtered

1193 candidates to 924 candidates (77.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1193	0	1193
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1193	5	1198

Merged error: 0b

Counts

1198 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x) (/ (* (pow a (- t 1.0)) (pow z y)) (exp b)))
0.1b	(pow a (- t 1.0))
0.5b	(/ (* (pow a (- t 1.0)) (pow z y)) (exp b))
1.4b	(/ (* (- x) (/ (* (pow a (- t 1.0)) (pow z y)) (exp b))) (* -1 y))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-exp-log`
81×	`prod-exp`
64×	`div-exp`
50×	`add-cbrt-cube`
25×	`pow-to-exp` `pow-exp`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
11×	`unpow-prod-up`
10×	`associate-l`
9×	`prod-diff`
7×	`pow1` `times-frac` `associate-r`
5×	`pow-unpow`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `unpow-prod-down` `distribute-rgt-neg-in` `div-inv`
2×	`distribute-lft-neg-out` `frac-2neg` `associate-r/` `clear-num` `associate-/l/` `associate-/l` `pow-sub`
1×	`neg-mul-1` `sub-neg` `pow-pow` `distribute-frac-neg` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 159

Calls

4 calls:

14.0ms	(* (- x) (/ (* (pow a (- t 1.0)) (pow z y)) (exp b)))
10.0ms	(pow a (- t 1.0))
11.0ms	(/ (* (pow a (- t 1.0)) (pow z y)) (exp b))
15.0ms	(/ (* (- x) (/ (* (pow a (- t 1.0)) (pow z y)) (exp b))) (* -1 y))

series682.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (- x) (/ (* (pow a (- t 1.0)) (pow z y)) (exp b)))
60.0ms	(pow a (- t 1.0))
185.0ms	(/ (* (pow a (- t 1.0)) (pow z y)) (exp b))
229.0ms	(/ (* (- x) (/ (* (pow a (- t 1.0)) (pow z y)) (exp b))) (* -1 y))

simplify119.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	915	1778
1	4786	1426
2	5001	1425

prune366.0ms

Filtered

171 candidates to 94 candidates (55.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	171	5	176

Merged error: 0b

Counts

176 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ y (* (pow a (- t 1.0)) (pow z y)))
0.1b	(pow a (- t 1.0))
1.0b	(/ x (* (/ y (* (pow a (- t 1.0)) (pow z y))) (exp b)))
1.5b	(* (/ y (* (pow a (- t 1.0)) (pow z y))) (exp b))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-exp-log`
49×	`prod-exp`
42×	`div-exp`
32×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`pow-to-exp` `add-cube-cbrt` `pow-exp`
11×	`unpow-prod-up`
10×	`cbrt-undiv`
9×	`times-frac` `prod-diff` `cbrt-unprod`
8×	`associate-l`
7×	`pow1`
6×	`associate-/l*`
5×	`pow-unpow`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `associate-r` `associate-/r/` `div-inv` `pow-sub`
2×	`frac-2neg` `clear-num` `associate-/r*`
1×	`sub-neg` `pow-pow` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 139

Calls

4 calls:

8.0ms	(/ y (* (pow a (- t 1.0)) (pow z y)))
5.0ms	(pow a (- t 1.0))
13.0ms	(/ x (* (/ y (* (pow a (- t 1.0)) (pow z y))) (exp b)))
17.0ms	(* (/ y (* (pow a (- t 1.0)) (pow z y))) (exp b))

series594.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ y (* (pow a (- t 1.0)) (pow z y)))
60.0ms	(pow a (- t 1.0))
199.0ms	(/ x (* (/ y (* (pow a (- t 1.0)) (pow z y))) (exp b)))
185.0ms	(* (/ y (* (pow a (- t 1.0)) (pow z y))) (exp b))

simplify77.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	766	1330
1	3128	1098
2	5001	1095

prune348.0ms

Filtered

151 candidates to 90 candidates (59.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	151	5	156

Merged error: 0b

Counts

156 → 5

regimes388.0ms

Accuracy

80.7% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 1.9b

bsearch360.0ms

Steps

Iters	Range		Point
7	304.0849354186872	8389.426513849796	8234.665933457405
8	-2.7372821165424347e+41	-3.2829900886244486e+38	-1.3375298747491056e+41

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	22
1	44	22

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.1s	45515×	body	80	nan
1.3s	15363×	body	80	valid