Details

sample62.0ms

Algorithm

intervals

Results

45.0ms

691×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0b	(+ (* a a) (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `unpow-prod-down` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `pow-to-exp` `pow-pow` `fma-def` `flip3-+` `pow-exp` `sum-log` `flip-+` `fma-udef` `sqr-pow`

Counts

3 → 43

Calls

3 calls:

0.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
3.0ms	(+ (* a a) (* b b))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series207.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
26.0ms	(+ (* a a) (* b b))
105.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify107.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	226	319
1	972	282
2	3693	275
3	5001	274

prune152.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a a (* b b))
0.0b	(fma a a (* b b))
0.0b	(fma (* 4.0 b) b (- (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) 1.0))
0.3b	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`unpow-prod-down`
16×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqr-pow`
9×	`prod-exp` `unswap-sqr`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`pow2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 84

Calls

4 calls:

0.0ms	(fma a a (* b b))
0.0ms	(fma a a (* b b))
0.0ms	(fma (* 4.0 b) b (- (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) 1.0))
12.0ms	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma a a (* b b))
33.0ms	(fma a a (* b b))
255.0ms	(fma (* 4.0 b) b (- (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) 1.0))
154.0ms	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

simplify40.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	214	833
1	917	718
2	5001	679

prune244.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot a b)
0.1b	(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
0.2b	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
9.4b	(sqrt (fma a a (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log`
66×	`prod-exp`
34×	`pow-to-exp` `pow-exp`
25×	`add-sqr-sqrt`
18×	`unpow-prod-down`
17×	`associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-cbrt-cube`
9×	`unswap-sqr` `sqr-pow`
8×	`associate-l`
6×	`sqrt-prod`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`rem-sqrt-square` `hypot-udef` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def`

Counts

4 → 122

Calls

4 calls:

0.0ms	(hypot a b)
16.0ms	(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
9.0ms	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
1.0ms	(sqrt (fma a a (* b b)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot a b)
240.0ms	(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
309.0ms	(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
44.0ms	(sqrt (fma a a (* b b)))

simplify64.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	552	1646
1	1922	1490
2	5002	1335

prune434.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))) (cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))))
19.0b	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))
19.0b	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))
19.0b	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`pow1` `cbrt-prod`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

9.0ms	(* (cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))) (cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))))
3.0ms	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))
3.0ms	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))
3.0ms	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))) (cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))))
159.0ms	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))
158.0ms	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))
159.0ms	(cbrt (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))))

simplify87.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	164	1186
1	538	1015
2	2387	911
3	5003	899

prune292.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	18
1	26	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

21017×

body

valid