Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* a c) (* b d))
23.0b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 47

Calls

2 calls:

4.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series110.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* a c) (* b d))
78.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify105.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	244	458
1	872	411
2	3164	403
3	5001	403

prune155.0ms

Filtered

53 candidates to 44 candidates (83.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a c (* b d))
0.0b	(/ 1 (* (hypot c d) 1))
0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
13.6b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
92×	`prod-exp`
63×	`div-exp`
50×	`add-cbrt-cube`
41×	`1-exp`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
15×	`rec-exp`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`pow1`
7×	`associate-r` `associate-l`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*`
1×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

1.0ms	(fma a c (* b d))
5.0ms	(/ 1 (* (hypot c d) 1))
11.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
4.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series369.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma a c (* b d))
54.0ms	(/ 1 (* (hypot c d) 1))
170.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
106.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify48.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	486	1191
1	1654	892
2	5002	884

prune272.0ms

Filtered

157 candidates to 77 candidates (49.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
13.6b	(/ (fma a c (* b d)) (hypot c d))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
4×	`prod-exp` `associate-/r*` `div-inv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

1.0ms	(fma a c (* b d))
7.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
3.0ms	(/ (fma a c (* b d)) (hypot c d))

series249.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(fma a c (* b d))
108.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
106.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify77.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670

prune258.0ms

Filtered

98 candidates to 76 candidates (77.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a c (* b d))
0.0b	(/ 1 (* (hypot c d) 1))
0.2b	(* (/ 1 (* (hypot c d) 1)) (* (fma a c (* b d)) (/ 1 (hypot c d))))
13.7b	(* (fma a c (* b d)) (/ 1 (hypot c d)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

208×	`add-exp-log`
130×	`prod-exp`
58×	`div-exp`
50×	`add-cbrt-cube`
47×	`1-exp`
29×	`rec-exp`
23×	`add-sqr-sqrt`
21×	`cbrt-unprod`
17×	`*-un-lft-identity` `times-frac`
16×	`add-cube-cbrt`
14×	`pow1` `associate-r`
12×	`cbrt-undiv`
10×	`associate-l`
5×	`associate-*r/` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv` `div-inv` `associate-/l*` `unswap-sqr`
2×	`frac-times` `pow-flip` `*-commutative`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `fma-udef` `inv-pow`

Counts

4 → 165

Calls

4 calls:

1.0ms	(fma a c (* b d))
5.0ms	(/ 1 (* (hypot c d) 1))
12.0ms	(* (/ 1 (* (hypot c d) 1)) (* (fma a c (* b d)) (/ 1 (hypot c d))))
7.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma a c (* b d))
53.0ms	(/ 1 (* (hypot c d) 1))
171.0ms	(* (/ 1 (* (hypot c d) 1)) (* (fma a c (* b d)) (/ 1 (hypot c d))))
112.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

simplify53.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	586	1348
1	1918	993
2	5001	973

prune268.0ms

Filtered

177 candidates to 79 candidates (44.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.8b

regimes153.0ms

Accuracy

18.8% (9.2b remaining)

Error of 15.1b against oracle of 6.0b and baseline of 17.2b

bsearch43.0ms

Steps

Iters	Range		Point
10	1.464110213656478e+115	6.0573437940032564e+125	5.882312647988265e+125

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	10
1	21	10
2	21	10

end0.0ms

sample513.0ms

Algorithm

intervals

Results

304.0ms

8456×

body

valid