Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

265×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.0b	(+ (* a c) (* b d))
24.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

3.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series147.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
33.0ms	(+ (* a c) (* b d))
84.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify139.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462

prune207.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (hypot c d) 1))
0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.5b	(fma a c (* b d))
13.4b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite37.0ms

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:

4.0ms	(/ 1 (* (hypot c d) 1))
21.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series390.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (* (hypot c d) 1))
183.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
40.0ms	(fma a c (* b d))
114.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify50.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	486	1199
1	1655	892
2	5001	884

prune290.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.5b	(fma a c (* b d))
13.4b	(/ (fma a c (* b d)) (hypot c d))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

0.0ms	(hypot c d)
6.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.0ms	(fma a c (* b d))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series320.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot c d)
119.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
40.0ms	(fma a c (* b d))
115.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify83.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	308	794
1	1149	701
2	3275	701
3	5001	693

prune309.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.1b	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
0.5b	(fma a c (* b d))
13.5b	(* (fma a c (* b d)) (/ 1 (hypot c d)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`add-cbrt-cube`
27×	`add-sqr-sqrt`
26×	`prod-exp`
25×	`div-exp`
21×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
13×	`associate-r`
10×	`cbrt-undiv` `1-exp`
9×	`cbrt-unprod`
7×	`pow1`
5×	`rec-exp`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `associate-/l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 119

Calls

4 calls:

2.0ms	(/ 1 (hypot c d))
7.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
0.0ms	(fma a c (* b d))
10.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (hypot c d))
117.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
37.0ms	(fma a c (* b d))
116.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

simplify45.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	394	872
1	1636	690
2	5001	663

prune236.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

regimes229.0ms

Accuracy

35.5% (7.0b remaining)

Error of 12.7b against oracle of 5.7b and baseline of 16.5b

bsearch69.0ms

Steps

Iters	Range		Point
5	2.6545994669624432e+182	1.0129075260036237e+183	5.2660357604755783e+182
9	-2.963931757502914e+119	-3.0087443311191178e+113	-1.0970461090118266e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	32	15
2	32	15

end0.0ms

sample510.0ms

Algorithm

intervals

Results

299.0ms

8481×

body

valid