Details

sample278.0ms

Algorithm

intervals

Results

128.0ms	1642×	body	80	nan
51.0ms	534×	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

prune12.0ms

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))
0.2b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.1b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite34.0ms

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))
4.0ms	(* y (log z))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
12.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series366.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (- t 1.0) (log a))
40.0ms	(* y (log z))
109.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
163.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify66.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (54.0ms)

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

prune361.0ms

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))
0.2b	(fma (log (/ 1 a)) t b)
1.1b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite45.0ms

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:

22.0ms	(* 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)
14.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series792.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
77.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
72.0ms	(fma (log (/ 1 a)) t b)
321.0ms	(/ (* 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 (71.0ms)

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

prune616.0ms

Filtered

165 candidates to 124 candidates (75.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	165	5	170

Merged error: 0.0b

Counts

170 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log (/ 1 a)) t b)
0.2b	(/ 1 (sqrt a))
0.2b	(/ 1 (sqrt a))
1.1b	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ 1 (sqrt a)) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

321×	`add-exp-log`
181×	`div-exp`
105×	`prod-exp`
60×	`pow-exp`
39×	`times-frac`
37×	`add-cbrt-cube`
36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
17×	`rec-exp` `1-exp`
15×	`pow-to-exp` `associate-/r*`
14×	`cbrt-undiv`
10×	`cbrt-unprod`
8×	`pow1`
7×	`associate-/l*`
6×	`pow-flip`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-*r/` `clear-num` `div-inv` `associate-/l/`
2×	`sqrt-pow1` `pow1/2` `inv-pow`
1×	`frac-times` `associate-*l/` `fma-udef`

Counts

4 → 190

Calls

4 calls:

1.0ms	(fma (log (/ 1 a)) t b)
4.0ms	(/ 1 (sqrt a))
4.0ms	(/ 1 (sqrt a))
50.0ms	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ 1 (sqrt a)) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series695.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(fma (log (/ 1 a)) t b)
33.0ms	(/ 1 (sqrt a))
27.0ms	(/ 1 (sqrt a))
554.0ms	(/ (* (* x (/ (pow (/ 1 (sqrt a)) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (pow (/ 1 (sqrt a)) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify91.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	1002	3352
1	3440	2249
2	5002	2107

prune551.0ms

Filtered

202 candidates to 84 candidates (41.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	202	5	207

Merged error: 0.0b

Counts

207 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt a))
0.2b	(/ 1 (sqrt a))
0.5b	(* (pow (/ 1 (sqrt a)) 1.0) (pow (/ 1 (sqrt a)) 1.0))
1.1b	(/ (* (- x) (/ (* (pow (/ 1 (sqrt a)) 1.0) (pow (/ 1 (sqrt a)) 1.0)) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (- y))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-exp-log`
224×	`add-sqr-sqrt`
186×	`times-frac`
174×	`unpow-prod-down`
130×	`*-un-lft-identity`
128×	`div-exp`
110×	`prod-exp`
100×	`add-cube-cbrt`
96×	`pow-exp`
94×	`sqrt-prod`
49×	`unswap-sqr`
34×	`swap-sqr`
26×	`rec-exp` `1-exp` `associate-r` `associate-l`
24×	`pow-to-exp` `add-cbrt-cube`
22×	`associate-/r*`
18×	`sqr-pow`
9×	`div-inv`
8×	`pow1` `cbrt-undiv`
7×	`associate-/l*`
6×	`distribute-lft-neg-in` `pow-flip` `distribute-rgt-neg-in`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`neg-mul-1` `sqrt-pow1` `pow1/2` `inv-pow`
1×	`distribute-lft-neg-out` `pow2` `associate-r/` `distribute-frac-neg` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l/`

Counts

4 → 358

Calls

4 calls:

5.0ms	(/ 1 (sqrt a))
5.0ms	(/ 1 (sqrt a))
26.0ms	(* (pow (/ 1 (sqrt a)) 1.0) (pow (/ 1 (sqrt a)) 1.0))
24.0ms	(/ (* (- x) (/ (* (pow (/ 1 (sqrt a)) 1.0) (pow (/ 1 (sqrt a)) 1.0)) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (- y))

series966.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (sqrt a))
28.0ms	(/ 1 (sqrt a))
345.0ms	(* (pow (/ 1 (sqrt a)) 1.0) (pow (/ 1 (sqrt a)) 1.0))
558.0ms	(/ (* (- x) (/ (* (pow (/ 1 (sqrt a)) 1.0) (pow (/ 1 (sqrt a)) 1.0)) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (- y))

simplify72.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1326	4123
1	5001	3616

prune1.2s

Filtered

370 candidates to 160 candidates (43.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	369	1	370
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	369	6	375

Merged error: 0b

Counts

375 → 6

regimes479.0ms

Accuracy

0% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.2s	45623×	body	80	nan
1.2s	15170×	body	80	valid