Details

sample175.0ms

Algorithm

intervals

Results

69.0ms	1396×	body	80	nan
33.0ms	494×	body	80	valid

simplify52.0ms

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:

0.2b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.3b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite38.0ms

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))
7.0ms	(* 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)

series381.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
118.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
170.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

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

prune391.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	122	4	126

Merged error: 0.0b

Counts

126 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))
0.2b	(fma (log (/ 1 a)) t b)
4.5b	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

3049×	`times-frac`
1216×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
728×	`unpow-prod-down`
241×	`fma-udef`
239×	`exp-sum`
144×	`div-inv`
72×	`associate-/l*`
56×	`sqr-pow`
39×	`add-exp-log`
37×	`div-exp`
16×	`add-cbrt-cube`
13×	`associate-/r*`
8×	`cbrt-undiv` `pow-exp`
5×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod`
2×	`pow-to-exp` `rec-exp` `1-exp`
1×	`frac-2neg` `clear-num` `associate-/r/` `rem-exp-log` `associate-/l/`

Counts

4 → 1087

Calls

4 calls:

2.0ms	(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)
39.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

series764.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))
84.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
77.0ms	(fma (log (/ 1 a)) t b)
515.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (/ y x))

simplify287.0ms

Algorithm

egg-herbie

Counts

1099 → 1099

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	28990

prune5.6s

Filtered

1099 candidates to 847 candidates (77.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1095	4	1099
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	1099	4	1103

Merged error: 0.0b

Counts

1103 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* (log (/ 1 z)) y) (+ (* (log (/ 1 a)) t) b)))
0.3b	(* (log (/ 1 a)) t)
0.3b	(* (log (/ 1 z)) y)
0.8b	(* (pow (/ 1 (pow a 1.0)) 1.0) (/ x (* (exp (+ (* (log (/ 1 z)) y) (+ (* (log (/ 1 a)) t) b))) y)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-exp-log`
50×	`prod-exp`
48×	`add-sqr-sqrt`
43×	`unpow-prod-down`
42×	`div-exp`
41×	`associate-l`
39×	`pow-exp`
30×	`times-frac`
29×	`*-un-lft-identity`
26×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r`
12×	`pow1` `pow-to-exp`
11×	`unswap-sqr`
10×	`add-log-exp`
9×	`rec-exp` `1-exp`
7×	`sqr-pow`
6×	`log-pow` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `sum-log` `*-commutative` `rem-exp-log`
2×	`cbrt-undiv` `distribute-lft-neg-out` `pow-flip` `log-rec` `pow-prod-down` `div-inv` `inv-pow`
1×	`associate-*r/` `exp-sum`

Counts

4 → 159

Calls

4 calls:

9.0ms	(exp (+ (* (log (/ 1 z)) y) (+ (* (log (/ 1 a)) t) b)))
5.0ms	(* (log (/ 1 a)) t)
9.0ms	(* (log (/ 1 z)) y)
25.0ms	(* (pow (/ 1 (pow a 1.0)) 1.0) (/ x (* (exp (+ (* (log (/ 1 z)) y) (+ (* (log (/ 1 a)) t) b))) y)))

series644.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(exp (+ (* (log (/ 1 z)) y) (+ (* (log (/ 1 a)) t) b)))
60.0ms	(* (log (/ 1 a)) t)
65.0ms	(* (log (/ 1 z)) y)
404.0ms	(* (pow (/ 1 (pow a 1.0)) 1.0) (/ x (* (exp (+ (* (log (/ 1 z)) y) (+ (* (log (/ 1 a)) t) b))) y)))

simplify85.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	758	2162
1	2786	1929
2	5001	1876

prune675.0ms

Filtered

171 candidates to 114 candidates (66.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	171	4	175

Merged error: 0b

Counts

175 → 4

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
0.8b	(/ (/ (pow (* (cbrt (/ 1 a)) (cbrt (/ 1 a))) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ (* (cbrt y) (cbrt y)) (* (cbrt x) (cbrt x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

445×	`times-frac`
155×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
120×	`sqrt-prod`
114×	`add-exp-log`
65×	`div-exp`
47×	`div-inv`
42×	`unpow-prod-down` `sqr-pow`
39×	`associate-/l*`
30×	`exp-sum` `fma-udef`
29×	`add-cbrt-cube`
25×	`prod-exp`
23×	`cbrt-undiv`
10×	`pow-exp`
9×	`cbrt-prod`
8×	`cbrt-unprod`
5×	`pow-to-exp` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`frac-2neg` `clear-num` `associate-/r/` `associate-/l/`

Counts

4 → 327

Calls

4 calls:

1.0ms	(cbrt x)
5.0ms	(cbrt x)
1.0ms	(cbrt x)
23.0ms	(/ (/ (pow (* (cbrt (/ 1 a)) (cbrt (/ 1 a))) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ (* (cbrt y) (cbrt y)) (* (cbrt x) (cbrt x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
185.0ms	(cbrt x)
177.0ms	(cbrt x)
590.0ms	(/ (/ (pow (* (cbrt (/ 1 a)) (cbrt (/ 1 a))) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ (* (cbrt y) (cbrt y)) (* (cbrt x) (cbrt x))))

simplify126.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1760	11270
1	5002	10507

prune2.4s

Filtered

339 candidates to 241 candidates (71.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	339	0	339
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	339	4	343

Merged error: 0b

Counts

343 → 4

regimes206.0ms

Accuracy

0% (1.5b remaining)

Error of 1.5b against oracle of 0.0b and baseline of 1.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	40
1	34	40

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.4s	46051×	body	80	nan
932.0ms	15281×	body	80	valid