Details

sample252.0ms

Algorithm

intervals

Results

120.0ms	1546×	body	80	nan
53.0ms	529×	body	80	valid

simplify54.0ms

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

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))
0.8b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
1.2b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite135.0ms

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:

12.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
82.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
33.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series382.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
168.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
115.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (51.0ms)

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

prune621.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)
0.2b	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
0.8b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

116×	`times-frac`
65×	`unpow-prod-down`
64×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
33×	`add-exp-log`
24×	`div-exp`
20×	`fma-udef`
18×	`exp-sum` `associate-/l*`
15×	`add-cbrt-cube`
8×	`pow-exp`
7×	`prod-exp` `associate-/r*` `div-inv`
5×	`cbrt-undiv` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`associate-*r/` `associate-/l/`

Counts

4 → 159

Calls

4 calls:

0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
13.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
13.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series798.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
78.0ms	(fma (log (/ 1 a)) t b)
296.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
342.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify78.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	746	2775
1	2943	2527
2	5003	2512

prune694.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)
0.2b	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
0.8b	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
110×	`add-exp-log`
69×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
65×	`unpow-prod-down`
60×	`prod-exp`
56×	`div-exp`
27×	`add-cbrt-cube`
20×	`pow-exp` `fma-udef`
18×	`exp-sum`
17×	`associate-/l*`
13×	`rec-exp` `1-exp` `associate-r`
10×	`cbrt-unprod`
9×	`pow1`
7×	`div-inv`
6×	`cbrt-undiv`
5×	`pow-to-exp` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `pow-prod-down`
1×	`frac-times` `frac-2neg` `associate-l` `associate-l/` `clear-num` `un-div-inv` `-commutative`

Counts

4 → 196

Calls

4 calls:

0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
13.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
49.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

series778.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
77.0ms	(fma (log (/ 1 a)) t b)
287.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
337.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

simplify104.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	962	3373
1	4029	3038
2	5003	2899

prune665.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow (/ 1 a) 1.0))
0.6b	(cbrt (pow (/ 1 a) 1.0))
0.6b	(cbrt (pow (/ 1 a) 1.0))
0.8b	(* (* x (* (/ (* (cbrt (pow (/ 1 a) 1.0)) (cbrt (pow (/ 1 a) 1.0))) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (cbrt (pow (/ 1 a) 1.0)) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ 1 y))

rewrite793.0ms

Algorithm

rewrite-expression-head

Rules

280×	`add-exp-log`
164×	`prod-exp`
96×	`add-cbrt-cube`
82×	`cbrt-unprod`
76×	`div-exp`
51×	`cbrt-prod`
39×	`unpow-prod-down`
38×	`cbrt-undiv`
36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `associate-r`
12×	`rec-exp` `1-exp`
9×	`associate-*r/`
6×	`pow-prod-down`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow1/3` `sqr-pow`
1×	`associate-l` `un-div-inv` `*-commutative`

Counts

4 → 188

Calls

4 calls:

3.0ms	(cbrt (pow (/ 1 a) 1.0))
3.0ms	(cbrt (pow (/ 1 a) 1.0))
3.0ms	(cbrt (pow (/ 1 a) 1.0))
771.0ms	(* (* x (* (/ (* (cbrt (pow (/ 1 a) 1.0)) (cbrt (pow (/ 1 a) 1.0))) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (cbrt (pow (/ 1 a) 1.0)) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ 1 y))

series1.4s

Counts

4 → 12

Calls

4 calls:

354.0ms	(cbrt (pow (/ 1 a) 1.0))
373.0ms	(cbrt (pow (/ 1 a) 1.0))
352.0ms	(cbrt (pow (/ 1 a) 1.0))
336.0ms	(* (* x (* (/ (* (cbrt (pow (/ 1 a) 1.0)) (cbrt (pow (/ 1 a) 1.0))) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (cbrt (pow (/ 1 a) 1.0)) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ 1 y))

simplify73.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1265	6040
1	5002	3835

prune810.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes256.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.4s	45587×	body	80	nan
1.6s	15220×	body	80	valid