Details

sample35.0ms

Algorithm

intervals

Results

17.0ms

268×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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:

6.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series112.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* a c) (* b d))
77.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify94.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

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

prune155.0ms

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))

rewrite26.0ms

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))
4.0ms	(/ 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))

series376.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma a c (* b d))
50.0ms	(/ 1 (* (hypot c d) 1))
175.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
112.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify49.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (36.0ms)

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

prune279.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize19.0ms

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))

rewrite17.0ms

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))
8.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
6.0ms	(/ (fma a c (* b d)) (hypot c d))

series259.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma a c (* b d))
111.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
112.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify83.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (74.0ms)

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

prune258.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

212×	`add-exp-log`
130×	`prod-exp`
60×	`div-exp`
52×	`add-cbrt-cube`
48×	`1-exp`
31×	`add-sqr-sqrt`
30×	`rec-exp`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`cbrt-unprod`
20×	`associate-l`
15×	`pow1`
13×	`cbrt-undiv`
6×	`fma-udef` `associate-/l*`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `associate-r` `associate-l/` `associate-/r` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative` `inv-pow`
1×	`frac-times` `associate-*r/`

Counts

4 → 191

Calls

4 calls:

3.0ms	(/ 1 (hypot c d))
4.0ms	(/ 1 (* (hypot c d) 1))
14.0ms	(* (/ 1 (* (hypot c d) 1)) (* (/ 1 (hypot c d)) (fma a c (* b d))))
7.0ms	(* (/ 1 (hypot c d)) (fma a c (* b d)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1 (hypot c d))
54.0ms	(/ 1 (* (hypot c d) 1))
177.0ms	(* (/ 1 (* (hypot c d) 1)) (* (/ 1 (hypot c d)) (fma a c (* b d))))
134.0ms	(* (/ 1 (hypot c d)) (fma a c (* b d)))

simplify62.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	675	1500
1	2309	1125
2	5001	1046

prune303.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

regimes178.0ms

Accuracy

35% (8.2b remaining)

Error of 12.8b against oracle of 4.6b and baseline of 17.2b

bsearch126.0ms

Steps

Iters	Range		Point
10	1.464110213656478e+115	6.0573437940032564e+125	2.2413672752256256e+125
9	-3.9788200308749486e+18	-5288626288997.5625	-86223460658051.5
9	-1.2571754799481663e+163	-4.544732995620792e+155	-2.945998009177675e+158

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	27
1	45	27
2	45	27

end0.0ms

sample503.0ms

Algorithm

intervals

Results

298.0ms

8456×

body

valid