Details

sample206.0ms

Algorithm

intervals

Results

70.0ms	1457×	body	80	nan
33.0ms	499×	body	80	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	33	10
1	73	10
2	197	8
3	558	8
4	2287	8
5	5001	8

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.6b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite302.0ms

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:

26.0ms	(* (- t 1.0) (log a))
9.0ms	(* y (log z))
79.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
185.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series406.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- t 1.0) (log a))
38.0ms	(* y (log z))
123.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
185.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify59.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

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

prune426.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

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)
1.6b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite89.0ms

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:

55.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
25.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series912.0ms

Counts

4 → 12

Calls

4 calls:

372.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
86.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
85.0ms	(fma (log (/ 1 a)) t b)
369.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify95.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (76.0ms)

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

prune747.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
0.3b	(/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.5b	(/ x (/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

3407×	`times-frac`
1391×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
832×	`unpow-prod-down`
293×	`associate-/r*`
274×	`fma-udef`
272×	`exp-sum`
86×	`div-inv`
64×	`sqr-pow`
41×	`add-exp-log`
38×	`div-exp`
18×	`add-cbrt-cube`
9×	`cbrt-undiv`
8×	`pow-exp`
6×	`associate-/r/` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `clear-num`

Counts

4 → 1244

Calls

4 calls:

0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
36.0ms	(/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
73.0ms	(/ x (/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
83.0ms	(fma (log (/ 1 a)) t b)
276.0ms	(/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
371.0ms	(/ x (/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

simplify336.0ms

Algorithm

egg-herbie

Counts

1256 → 1256

Iterations

Useful iterations: 1 (80.0ms)

Iter	Nodes	Cost
0	4928	30290
1	5001	30288

prune7.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log (/ 1 a)) t b)
0.1b	(fma (log (/ 1 a)) t b)
0.3b	(sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.3b	(sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
144×	`sqrt-prod`
126×	`add-sqr-sqrt`
110×	`unpow-prod-down`
106×	`*-un-lft-identity`
104×	`add-cube-cbrt`
36×	`fma-udef`
34×	`exp-sum`
12×	`rem-sqrt-square`
10×	`div-inv` `sqr-pow`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 200

Calls

4 calls:

0.0ms	(fma (log (/ 1 a)) t b)
0.0ms	(fma (log (/ 1 a)) t b)
21.0ms	(sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
24.0ms	(sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))

series932.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma (log (/ 1 a)) t b)
76.0ms	(fma (log (/ 1 a)) t b)
387.0ms	(sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
387.0ms	(sqrt (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	562	4014
1	1589	3862
2	5002	3604

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes199.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	25
1	24	25

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.3s	47292×	body	80	nan
934.0ms	15305×	body	80	valid