Details

sample237.0ms

Algorithm

intervals

Results

109.0ms	1539×	body	80	nan
40.0ms	469×	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

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: 0.3b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.9b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite39.0ms

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:

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

series382.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (- t 1.0) (log a))
41.0ms	(* y (log z))
114.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
174.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify67.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (51.0ms)

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

prune416.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Merged error: 0.0b

Counts

126 → 5

localize20.0ms

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
74×	`add-sqr-sqrt`
72×	`associate-r`
58×	`*-un-lft-identity`
57×	`add-cube-cbrt`
55×	`unpow-prod-down`
41×	`add-exp-log`
24×	`div-exp`
19×	`fma-udef`
18×	`add-cbrt-cube`
17×	`exp-sum`
14×	`prod-exp`
8×	`pow-exp`
6×	`pow1` `div-inv` `unswap-sqr`
5×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*`
2×	`pow-to-exp` `rec-exp` `1-exp` `associate-*r/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 153

Calls

4 calls:

29.0ms	(* 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)
16.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series849.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(* 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))
76.0ms	(fma (log (/ 1 a)) t b)
345.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify96.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	904	2177
1	4141	1915
2	5001	1905

prune700.0ms

Filtered

165 candidates to 124 candidates (75.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	161	4	165
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	164	6	170

Merged error: 0.0b

Counts

170 → 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)
0.3b	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

1173×	`times-frac`
526×	`add-sqr-sqrt`
502×	`*-un-lft-identity`
501×	`add-cube-cbrt`
367×	`unpow-prod-down`
220×	`associate-r`
121×	`fma-udef`
119×	`exp-sum`
72×	`associate-/l*`
41×	`add-exp-log`
37×	`div-inv`
30×	`div-exp`
29×	`sqr-pow`
18×	`add-cbrt-cube`
8×	`pow-exp` `prod-exp`
7×	`unswap-sqr`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `rec-exp` `1-exp`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 586

Calls

4 calls:

23.0ms	(/ (/ (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)
69.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

series797.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
78.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
74.0ms	(fma (log (/ 1 a)) t b)
334.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

simplify142.0ms

Algorithm

egg-herbie

Counts

598 → 598

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2443	10914
1	5001	10493

prune2.6s

Filtered

598 candidates to 447 candidates (74.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	595	3	598
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	598	6	604

Merged error: 0b

Counts

604 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series801.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(* (cbrt y) (cbrt y))
215.0ms	(cbrt y)
175.0ms	(cbrt y)
171.0ms	(cbrt y)

simplify86.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune452.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	93	6	99

Merged error: 0b

Counts

99 → 6

regimes270.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	30
1	28	30

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.2s	45707×	body	80	nan
1.3s	15256×	body	80	valid