Details

sample178.0ms

Algorithm

intervals

Results

78.0ms	1461×	body	80	nan
28.0ms	463×	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: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.9b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite37.0ms

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))
5.0ms	(* y (log z))
12.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
10.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

series389.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- t 1.0) (log a))
38.0ms	(* y (log z))
173.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
119.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

simplify63.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (52.0ms)

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

prune422.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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)
0.9b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite52.0ms

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:

27.0ms	(* 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)
15.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series854.0ms

Counts

4 → 12

Calls

4 calls:

350.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
85.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
80.0ms	(fma (log (/ 1 a)) t b)
339.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify97.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (77.0ms)

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

prune743.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (/ (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)
0.5b	(/ x (/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

rewrite211.0ms

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:

19.0ms	(/ y (/ (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)
52.0ms	(/ x (/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

series792.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
87.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
83.0ms	(fma (log (/ 1 a)) t b)
357.0ms	(/ x (/ y (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))

simplify357.0ms

Algorithm

egg-herbie

Counts

1256 → 1256

Iterations

Useful iterations: 1 (84.0ms)

Iter	Nodes	Cost
0	4928	30290
1	5001	30288

prune7.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))
0.2b	(sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
0.2b	(sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
0.9b	(/ (* (* x (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

223×	`sqrt-prod`
222×	`times-frac`
155×	`add-sqr-sqrt`
144×	`associate-r`
117×	`*-un-lft-identity`
115×	`add-cube-cbrt`
97×	`unpow-prod-down`
38×	`add-exp-log` `add-cbrt-cube`
22×	`exp-sum` `fma-udef`
13×	`cbrt-undiv` `div-exp` `unswap-sqr`
12×	`prod-exp` `cbrt-unprod`
9×	`div-inv` `sqr-pow`
8×	`pow1` `sqrt-pow1`
6×	`exp-prod`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*` `associate-/l/`
2×	`rem-sqrt-square` `pow1/2`
1×	`frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l*`

Counts

4 → 250

Calls

4 calls:

41.0ms	(* x (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))
2.0ms	(sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
3.0ms	(sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
36.0ms	(/ (* (* x (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series1.0s

Counts

4 → 12

Calls

4 calls:

395.0ms	(* x (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))
153.0ms	(sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
148.0ms	(sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
352.0ms	(/ (* (* x (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify65.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1158	4496
1	5002	3775

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes195.0ms

Accuracy

0% (1.2b remaining)

Error of 1.3b against oracle of 0.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	12
1	21	12

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.4s	45345×	body	80	nan
948.0ms	15161×	body	80	valid