Details

sample53.0ms

Algorithm

intervals

Results

26.0ms

487×

body

valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	33	9
1	87	9
2	260	8
3	872	8
4	2436	8
5	4957	8
6	5001	8

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x y (* z t))
0.0b	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
4.8b	(* (- (fma c b a)) (* c i))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-l`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`distribute-lft-neg-out` `neg-mul-1` `associate-r` `*-commutative`

Counts

3 → 48

Calls

3 calls:

1.0ms	(fma x y (* z t))
1.0ms	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
6.0ms	(* (- (fma c b a)) (* c i))

series837.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma x y (* z t))
726.0ms	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
69.0ms	(* (- (fma c b a)) (* c i))

simplify137.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	216	334
1	818	287
2	4379	281
3	5001	279

prune257.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b	(cbrt (fma c b a))
1.8b	(cbrt (fma c b a))
1.8b	(cbrt (fma c b a))
2.8b	(* (* (cbrt (fma c b a)) (cbrt (fma c b a))) (* (- (cbrt (fma c b a))) (* c i)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-exp-log`
19×	`add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`distribute-lft-neg-out` `associate-r` `associate-l` `*-commutative` `distribute-rgt-neg-out`

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt (fma c b a))
1.0ms	(cbrt (fma c b a))
1.0ms	(cbrt (fma c b a))
13.0ms	(* (* (cbrt (fma c b a)) (cbrt (fma c b a))) (* (- (cbrt (fma c b a))) (* c i)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (fma c b a))
126.0ms	(cbrt (fma c b a))
125.0ms	(cbrt (fma c b a))
70.0ms	(* (* (cbrt (fma c b a)) (cbrt (fma c b a))) (* (- (cbrt (fma c b a))) (* c i)))

simplify57.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	304	695
1	1399	522
2	5001	440

prune395.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (pow (- (cbrt (fma c b a))) 3) (* c i))))
0.7b	(pow (- (cbrt (fma c b a))) 3)
1.8b	(cbrt (fma c b a))
4.8b	(* (pow (- (cbrt (fma c b a))) 3) (* c i))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

38×	`associate-l`
32×	`unpow-prod-down` `cube-prod`
27×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
18×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`prod-exp`
5×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow-exp` `cbrt-unprod`
2×	`cube-mult` `unpow3` `cube-neg` `sqr-pow`
1×	`distribute-lft-neg-out` `pow-pow` `pow1/3` `associate-r` `*-commutative` `fma-udef` `rem-cube-cbrt`

Counts

4 → 133

Calls

4 calls:

1.0ms	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (pow (- (cbrt (fma c b a))) 3) (* c i))))
5.0ms	(pow (- (cbrt (fma c b a))) 3)
1.0ms	(cbrt (fma c b a))
12.0ms	(* (pow (- (cbrt (fma c b a))) 3) (* c i))

series1.1s

Counts

4 → 12

Calls

4 calls:

736.0ms	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (pow (- (cbrt (fma c b a))) 3) (* c i))))
166.0ms	(pow (- (cbrt (fma c b a))) 3)
126.0ms	(cbrt (fma c b a))
70.0ms	(* (pow (- (cbrt (fma c b a))) 3) (* c i))

simplify90.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	509	861
1	2636	774
2	5001	761

prune510.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i)))))
4.8b	(* (- (fma c b a)) (* c i))
4.8b	(* (- (fma c b a)) (* c i))
4.8b	(* (- (fma c b a)) (* c i))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

30×	`associate-l`
19×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-out` `cbrt-prod` `neg-mul-1` `associate-r` `*-commutative`
1×	`pow1/3`

Counts

4 → 97

Calls

4 calls:

1.0ms	(cbrt (fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i)))))
6.0ms	(* (- (fma c b a)) (* c i))
6.0ms	(* (- (fma c b a)) (* c i))
6.0ms	(* (- (fma c b a)) (* c i))

series439.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(cbrt (fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i)))))
69.0ms	(* (- (fma c b a)) (* c i))
63.0ms	(* (- (fma c b a)) (* c i))
69.0ms	(* (- (fma c b a)) (* c i))

simplify127.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	253	694
1	874	612
2	4347	590
3	5003	588

prune715.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 1.2b

regimes601.0ms

Accuracy

-24.1% (1.5b remaining)

Error of 2.3b against oracle of 0.8b and baseline of 2.0b

bsearch183.0ms

Steps

Iters	Range		Point
10	1.1588542209622891e-241	9.900821582273777e-227	1.5793105327025385e-239
9	-8.304173047101669e-234	-1.3849507434735772e-242	-2.2953582784698825e-240

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	18
1	59	18
2	60	18
3	60	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

727.0ms

15106×

body

valid